本研究探討常用的兩個無母數迴歸方法，核迴歸與樣條迴歸，在具有傘型限制式下，對於傘型函數的估計與不具限制式下的傘型函數估計比較，同時也探討不同誤差變異對估計結果的影響，並進一步探討受限制下兩方法的估計比較。本研究採用「估計頂點位置與實際頂點位置差」及「誤差平方和」作為衡量估計結果的指標。在帶寬及節點的選取上，本研究採用逐一剔除交互驗證法來篩選。模擬結果顯示，受限制的核函數在誤差變異較大的頂點位置估計較佳，誤差變異縮小時反而頂點位置估計較差，受限制的B-樣條函數也有類似的狀況。而在兩方法的比較上，對於較小的誤差變異，核函數的頂點位置估計能力不如樣條函數，但在整體的誤差平方和上卻沒有太大劣勢，當誤差變異較大時，核函數的頂點位置估計能力有所提升，整體誤差平方和仍舊維持還不錯的結果。 / In this study, we give an umbrella order constraint on kernel and spline regression model. We compare their estimation in two measurements, one is the difference of estimate peak and true peak, the other one is the sum of square difference on predict and the true value. We use leave-one-out cross validation to select bandwidth for kernel function and also to decide the number of knots for spline function. The effect of different error size is also considered. Some of R packages are used when doing simulation. The result shows that when the error size is bigger, the prediction of peak location is better in both constrained kernel and spline estimation. The constrained spline regression tends to provide better peak location estimation compared to constrained kernel regression.

Existe uma grande e crescente literatura sobre especificação e estimação de fronteiras de produção e, portanto, de eficiência de unidades produtivas. Nesta tese, o foco esta sobre modelos de fronteiras determinísticas, os quais são baseados na hipótese de que os dados observados pertencem ao conjunto tecnológico. Dentre os modelos estatísticos e estimadores para fronteiras determinísticas existentes, uma abordagem promissora e a adotada por Martins-Filho e Yao (2007). Esses autores propõem um procedimento de estimação composto por três estágios. Esse estimador e de fácil implementação, visto que envolve procedimentos não-paramétricos bem conhecidos. Além disso, o estimador possui características desejáveis vis-à-vis estimadores para fronteiras determinísticas tradicionais como DEA e FDH. Nesta tese, três artigos, que melhoram o modelo proposto por Martins-Filho e Yao (2007), sao propostos. No primeiro artigo, o procedimento de estimação desses autores e melhorado a partir de uma variação do estimador exponencial local, proposto por Ziegelmann (2002). Demonstra-se que estimador proposto a consistente e assintoticamente normal. Além disso, devido ao estimador exponencial local, estimativas potencialmente negativas para a função de variância condicional, que poderiam prejudicar a aplicabilidade do estimador proposto por Martins-Filho e Yao, são evitadas. No segundo artigo, e proposto um método original para estimação de fronteiras de produção em apenas dois estágios. E mostrado que se pode eliminar o segundo estágio proposto por Martins-Filho e Yao, assim como, eliminar o segundo estagio proposto no primeiro artigo desta tese. Em ambos os casos, a estimação do mesmo modelo de fronteira de produção requer três estágios, sendo versões diferentes para o segundo estagio. As propriedades assintóticas do estimador proposto são analisadas, mostrando-se consistência e normalidade assintótica sob hipóteses razoáveis. No terceiro artigo, a proposta uma variação semi-paramétrica do modelo estudado no segundo artigo. Reescreve-se aquele modelo de modo que se possa estimar a fronteira de produção e a eficiência de unidades produtivas no contexto de múltiplos insumos, sem incorrer no curse of dimensionality. A abordagem adotada coloca o modelo na estrutura de modelos aditivos, a partir de hipóteses sobre como os insumos se combinam no processo produtivo. Em particular, considera-se aqui os casos de insumos aditivos e insumos multiplicativos, os quais são amplamente considerados em teoria econômica e aplicações. Estudos de Monte Carlo são apresentados em todos os artigos, afim de elucidar as propriedades dos estimadores propostos em amostras finitas. Além disso, estudos com dados reais são apresentados em todos os artigos, nos quais são estimador rankings de eficiência para uma amostra de departamentos policiais dos EUA, a partir de dados sobre criminalidade daquele país. / There exists a large and growing literature on the specification and estimation of production frontiers and therefore efficiency of production units. In this thesis we focus on deterministic production frontier models, which are based on the assumption that all observed data lie in the technological set. Among the existing statistical models and estimators for deterministic frontiers, a promising approach is that of Martins-Filho and Yao (2007). They propose an estimation procedure that consists of three stages. Their estimator is fairly easy to implement as it involves standard nonparametric procedures. In addition, it has a number of desirable characteristics vis-a-vis traditional deterministic frontier estimators as DEA and FDH. In this thesis we propose three papers that improve the model proposed in Martins-Filho and Yao (2007). In the first paper we improve their estimation procedure by adopting a variant of the local exponential smoothing proposed in Ziegelmann (2002). Our estimator is shown to be consistent and asymptotically normal. In addition, due to local exponential smoothing, potential negativity of conditional variance functions that may hinder the use of Martins-Filho and Yao's estimator is avoided. In the second paper we propose a novel method for estimating production frontiers in only two stages. (Continue). There we show that we can eliminate the second stage of Martins-Filho and Yao as well as of our first paper, where estimation of the same frontier model requires three stages under different versions for the second stage. We study asymptotic properties showing consistency andNirtnin, asymptotic normality of our proposed estimator under standard assumptions. In the third paper we propose a semiparametric variation of the frontier model studied in the second paper. We rewrite that model allowing for estimating the production frontier and efficiency of production units in a multiple input context without suffering the curse of dimensionality. Our approach places that model within the framework of additive models based on assumptions regarding the way inputs combine in production. In particular, we consider the cases of additive and multiplicative inputs, which are widely considered in economic theory and applications. Monte Carlo studies are performed in all papers to shed light on the finite sample properties of the proposed estimators. Furthermore a real data study is carried out in all papers, from which we rank efficiency within a sample of USA Law Enforcement agencies using USA crime data.

<p>The use of marketing research panels are a more and more frequently used source of information for studies within many different branches. The purpose of this report is to investigate the demographic composition of panels and compare it with the population of Sweden, a possible change in behaviour of respondents, and if the source of recruitment is the cause of possible differences in study results. The study was commissioned by Norstats Linkoping office. Sources for the data material include Norstat’s recruitment process and their two main panels with different recruitment sources. To enable a deeper investigation of behaviour we also constructed a survey that was sent to 2,714 members of Norstat’s internet panels.</p><p>The statistical analysis includes contingency table analysis, multiple logistic regression, and Poisson regression. The results show that the demographic composition does not fully cover all the aspects of the Swedish population and some groups are less represented than others. The behaviour tends to differ between panel members that have responded to three or less surveys compared to members that have responded to twenty or more surveys. Source of recruitment does not seem to affect the results of studies, but it has some effect on the demographic composition of marketing research panels.</p> / <p>Användandet av paneler som källa vid undersökningar har den senaste tiden blivit en allt vanligare företeelse. Denna rapport har för avsikt att undersöka panelers demografiska sammansättning och överensstämmande med Sveriges befolkning, eventuell ändring av svarsbeteende samt huruvida rekryteringskällan ger upphov till kvalitetsskillnader hos medlemmar i en panel. Företaget Norstat har med sitt kontor i Linköping figurerat som uppdragsgivare till arbetet. Datamaterialet till studien har uppkommit från Norstats rekryteringsprocess samt från företagets två huvudpaneler med olika rekryteringskällor. För att djupare undersöka svarsbeteende konstruerade vi även en enkätundersökning som skickades ut till 2 714 medlemmar i Norstats internetpaneler.</p><p>Den statiska analysen innefattar χ2-test, multipel logistisk regression samt Poissonregression. Resultaten påvisade att den demografiska sammansättningen i panelen inte fullt ut speglade Sveriges befolkning samt att vissa grupper undertäcks i högre utsträckning än andra. Svarsbeteendet hos medlemmar i paneler har en tendens att ändras från det att medlemmen har svarat på en till tre undersökningar, till det att den har svarat på tjugo undersökningar eller fler. Rekryteringskällan till en panel verkar inte ge upphov till några större skillnader i svarsresultat, men däremot finns vissa skillnader i demografisk sammansättning.</p>

In this thesis, we consider the problem of estimating the regression function in location-scale regression models. This model assumes that the random vector (X,Y) satisfies Y = m(X) + s(X)e, where m(.) is an unknown location function (e.g. conditional mean, median, truncated mean,...), s(.) is an unknown scale function, and e is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. In the first part of the thesis, we assume that m(x) = E(Y|X=x) follows a polynomial model. A new estimation procedure for the unknown regression parameters is proposed, which extends the classical least squares procedure to censored data. The proposed method is inspired by the method of Buckley and James (1979), but is, unlike the latter method, a non-iterative procedure due to nonparametric preliminary estimation. The asymptotic normality of the estimators is established. Simulations are carried out for both methods and they show that the proposed estimators have usually smaller variance and smaller mean squared error than the Buckley-James estimators. For the second part, suppose that m(.)=E(Y|.) belongs to some parametric class of regression functions. A new estimation procedure for the true, unknown vector of parameters is proposed, that extends the classical least squares procedure for nonlinear regression to the case where the response is subject to censoring. The proposed technique uses new `synthetic' data points that are constructed by using a nonparametric relation between Y and X. The consistency and asymptotic normality of the proposed estimator are established, and the estimator is compared via simulations with an estimator proposed by Stute in 1999. In the third part, we study the nonparametric estimation of the regression function m(.). It is well known that the completely nonparametric estimator of the conditional distribution F(.|x) of Y given X=x suffers from inconsistency problems in the right tail (Beran, 1981), and hence the location function m(x) cannot be estimated consistently in a completely nonparametric way, whenever m(x) involves the right tail of F(.|x) (like e.g. for the conditional mean). We propose two alternative estimators of m(x), that do not share the above inconsistency problems. The idea is to make use of the assumed location-scale model, in order to improve the estimation of F(.|x), especially in the right tail. We obtain the asymptotic properties of the two proposed estimators of m(x). Simulations show that the proposed estimators outperform the completely nonparametric estimator in many cases.

During 2006 an estimated number of 150 persons are supposed to have been killed in road accidents caused by speed limit violations. Through Automatic traffic security control (ATK) the Swedish road administration (Vägverket) is working towards lowering the number of speed related accidents. By placing the speed cameras on roads they've managed to lower the average speed at those places. The enlargement of the number of speed cameras is based upon knowledge about for example how high the risk is for speed related accidents on the roads. The speed cameras always measure the speed in which every vehicle passes, but aren't constantly activated to register speed violations. Our purpose with this essay is consequently to explore possible relations between the activation of the speed cameras and the speed itself on the roads.We studied the average speed and the number of speed violations during 12 weeks evenly distributed in 2007. To see if the results would differ, we used two different response variables in the analysis.  Multiple linear regression was used to analyse the average speed, while Poisson regression was used in the analysis of the number of speed violations. An activated camera proved to cause a lowered average speed and fewer speed violations in three regions (Skåne, Mälardalen, Norr).To study the effect of maximized camera activation, an experiment in the region of Mälardalen was performed in the beginning of 2008. The result showed that maximized camera activation didn't decelerate the average speed, in stead the region's own activation policy seems to be more important for a lowered average speed. When the traffic flow rises the average speed decelerates while the number of speed violations also rises. During the study of commuter traffic we could see that the average speed is lower and there is fewer speed violations on commuter roads compared to normal traffic roads. / Under 2006 beräknas 150 personer ha omkommit i vägtrafikolyckor på grund av överskridna hastighetsgränser. Vägverket arbetar för att sänka dessa siffror bland annat genom att använda sig av Automatisk trafiksäkerhetskontroll (ATK). Genom att placera trafiksäkerhetskameror på sträckor har medelhastigheten på dessa sänkts. Trafiksäkerhetskamerorna mäter alltid hastigheten hos varje passerande fordon, men är inte konstant aktiverade för att registrera hastighetsöverträdelser. Nu vill man optimera kameraaktiveringen för att minska antalet ärenden utan att hanteringskapaciteten överskrids. Vårt syfte med uppsatsen är därför att undersöka möjliga samband mellan aktivering av trafiksäkerhetskameror och själva hastigheten på vägarna.Medelhastigheten och antalet överträdelser studerades under tolv veckor jämnt fördelade över år 2007. Analyserna gjordes med två olika responsvariabler för att se om resultaten skilde sig åt. Vi använde oss av multipel linjär regression för att analysera medelhastigheten, medan Poissonregression användes för antalet överträdelser. Det visade sig att en aktiv kamera gav upphov till sänkta medelhastigheter och färre hastighetsöverträdelser i tre regioner (Skåne, Mälardalen, Norr).För att studera effekten av maximal kameraaktivering utfördes ett experiment i region Mälardalen under början av 2008. Det visade sig att en maximal aktivering inte gav en sänkning av genomsnittshastigheterna, istället verkar regionens egen aktiverings-strategi ha större betydelse för sänkta genomsnittshastigheter.När fordonsflödet på alla sträckor ökar så minskar medelhastigheten medan antalet överträdelser ökar. För pendeltrafiksträckor är medelhastigheten lägre och det sker färre hastighetsöverträdelser än på normaltrafiksträckor.

<p>During 2006 an estimated number of 150 persons are supposed to have been killed in road accidents caused by speed limit violations. Through Automatic traffic security control (ATK) the Swedish road administration (Vägverket) is working towards lowering the number of speed related accidents. By placing the speed cameras on roads they've managed to lower the average speed at those places. The enlargement of the number of speed cameras is based upon knowledge about for example how high the risk is for speed related accidents on the roads. The speed cameras always measure the speed in which every vehicle passes, but aren't constantly activated to register speed violations. Our purpose with this essay is consequently to explore possible relations between the activation of the speed cameras and the speed itself on the roads.We studied the average speed and the number of speed violations during 12 weeks evenly distributed in 2007. To see if the results would differ, we used two different response variables in the analysis.  Multiple linear regression was used to analyse the average speed, while Poisson regression was used in the analysis of the number of speed violations. An activated camera proved to cause a lowered average speed and fewer speed violations in three regions (Skåne, Mälardalen, Norr).To study the effect of maximized camera activation, an experiment in the region of Mälardalen was performed in the beginning of 2008. The result showed that maximized camera activation didn't decelerate the average speed, in stead the region's own activation policy seems to be more important for a lowered average speed. When the traffic flow rises the average speed decelerates while the number of speed violations also rises. During the study of commuter traffic we could see that the average speed is lower and there is fewer speed violations on commuter roads compared to normal traffic roads.</p> / <p>Under 2006 beräknas 150 personer ha omkommit i vägtrafikolyckor på grund av överskridna hastighetsgränser. Vägverket arbetar för att sänka dessa siffror bland annat genom att använda sig av Automatisk trafiksäkerhetskontroll (ATK). Genom att placera trafiksäkerhetskameror på sträckor har medelhastigheten på dessa sänkts. Trafiksäkerhetskamerorna mäter alltid hastigheten hos varje passerande fordon, men är inte konstant aktiverade för att registrera hastighetsöverträdelser. Nu vill man optimera kameraaktiveringen för att minska antalet ärenden utan att hanteringskapaciteten överskrids. Vårt syfte med uppsatsen är därför att undersöka möjliga samband mellan aktivering av trafiksäkerhetskameror och själva hastigheten på vägarna.Medelhastigheten och antalet överträdelser studerades under tolv veckor jämnt fördelade över år 2007. Analyserna gjordes med två olika responsvariabler för att se om resultaten skilde sig åt. Vi använde oss av multipel linjär regression för att analysera medelhastigheten, medan Poissonregression användes för antalet överträdelser. Det visade sig att en aktiv kamera gav upphov till sänkta medelhastigheter och färre hastighetsöverträdelser i tre regioner (Skåne, Mälardalen, Norr).För att studera effekten av maximal kameraaktivering utfördes ett experiment i region Mälardalen under början av 2008. Det visade sig att en maximal aktivering inte gav en sänkning av genomsnittshastigheterna, istället verkar regionens egen aktiverings-strategi ha större betydelse för sänkta genomsnittshastigheter.När fordonsflödet på alla sträckor ökar så minskar medelhastigheten medan antalet överträdelser ökar. För pendeltrafiksträckor är medelhastigheten lägre och det sker färre hastighetsöverträdelser än på normaltrafiksträckor.</p>

Due to the inherently hierarchical nature of many natural phenomena, data collected rests in nested entities. As an example, students are nested in schools, school are nested in districts, districts are nested in counties, and counties are nested within states. Multilevel models provide a statistical framework for investigating and drawing conclusions regarding the influence of factors at differing hierarchical levels of analysis. The work in this paper serves as an introduction to multilevel models and their comparison to Ordinary Least Squares (OLS) regression. We overview three basic model structures: variable intercept model, variable slope model, and hierarchical linear model and illustrate each model with an example of student data. Then, we contrast the three multilevel models with the OLS model and present a method for producing confidence intervals for the regression coefficients. / text

Mirtingumo nuo įvairių ligų įvertinimas ir prognozavimas pagal atlikto tyrimo duomenis – dažnas statistinės analizės uždavinys medicinoje. Juose siekiama prognozuoti tikėtiną mirčių nuo tiriamos ligos skaičių, susirgimo tam tikra liga tikimybę ar išskirti rizikos grupes, įvertinant tyrimo metu surinktų stebimos populiacijos imties kintamųjų duomenis ir nustatant, kokia priklausomybę juos sieja. Pagrindiniai šio darbo tikslai: susipažinti su statistikos metodais, taikomais mirtingumo duomenų analizei; sudaryti statistinės analizės modelius turimiems mirtingumo duomenims; realizuoti sudarytus modelius programiškai, panaudojant SAS sistemą ir SAS makro programavimo galimybes. Panaudojus Puasono, logistinės ir Kokso regresin��s analizės metodus sudaryti mirtingumo nuo galvos smegenų insulto (GSI) prognozavimo modeliai. Sudaryti modeliai realizuoti programiškai, panaudojus SAS programavimo kalbą, SAS/IML posistemės galimybes ir SAS makro programavimo priemones. Sukurti regresinės analizės modeliai ir programines priemonės panaudotos Kauno medicinos universiteto Kardiologijos instituto 1980-2004 metais atliktų tyrimų metu surinktų Kauno miesto 25-64 m. amžiaus gyventojų mirtingumo nuo GSI duomenų analizei atlikti. / Estimation and forecasting of mortality from various diseases are very frequent data analysis tasks in medicine nowadays. In order to estimate expected number of deaths, probability to die from a disease or trends in mortality we should apply the most suitable statistical methods. Data analysis models were created using Poisson, logistic, Cox regression methods and realized in SAS macros. Created software also contains models for goodness of fit analysis, graphical visualization and prepares a report of data analysis in RTF (Rich Text Format) format. Analysis was made for mortality from stroke data among Kaunas population aged 25 to 64 during the period 1980-2004. The study contains the description of applying created data analysis models, SAS macros and received results.

Existe uma grande e crescente literatura sobre especificação e estimação de fronteiras de produção e, portanto, de eficiência de unidades produtivas. Nesta tese, o foco esta sobre modelos de fronteiras determinísticas, os quais são baseados na hipótese de que os dados observados pertencem ao conjunto tecnológico. Dentre os modelos estatísticos e estimadores para fronteiras determinísticas existentes, uma abordagem promissora e a adotada por Martins-Filho e Yao (2007). Esses autores propõem um procedimento de estimação composto por três estágios. Esse estimador e de fácil implementação, visto que envolve procedimentos não-paramétricos bem conhecidos. Além disso, o estimador possui características desejáveis vis-à-vis estimadores para fronteiras determinísticas tradicionais como DEA e FDH. Nesta tese, três artigos, que melhoram o modelo proposto por Martins-Filho e Yao (2007), sao propostos. No primeiro artigo, o procedimento de estimação desses autores e melhorado a partir de uma variação do estimador exponencial local, proposto por Ziegelmann (2002). Demonstra-se que estimador proposto a consistente e assintoticamente normal. Além disso, devido ao estimador exponencial local, estimativas potencialmente negativas para a função de variância condicional, que poderiam prejudicar a aplicabilidade do estimador proposto por Martins-Filho e Yao, são evitadas. No segundo artigo, e proposto um método original para estimação de fronteiras de produção em apenas dois estágios. E mostrado que se pode eliminar o segundo estágio proposto por Martins-Filho e Yao, assim como, eliminar o segundo estagio proposto no primeiro artigo desta tese. Em ambos os casos, a estimação do mesmo modelo de fronteira de produção requer três estágios, sendo versões diferentes para o segundo estagio. As propriedades assintóticas do estimador proposto são analisadas, mostrando-se consistência e normalidade assintótica sob hipóteses razoáveis. No terceiro artigo, a proposta uma variação semi-paramétrica do modelo estudado no segundo artigo. Reescreve-se aquele modelo de modo que se possa estimar a fronteira de produção e a eficiência de unidades produtivas no contexto de múltiplos insumos, sem incorrer no curse of dimensionality. A abordagem adotada coloca o modelo na estrutura de modelos aditivos, a partir de hipóteses sobre como os insumos se combinam no processo produtivo. Em particular, considera-se aqui os casos de insumos aditivos e insumos multiplicativos, os quais são amplamente considerados em teoria econômica e aplicações. Estudos de Monte Carlo são apresentados em todos os artigos, afim de elucidar as propriedades dos estimadores propostos em amostras finitas. Além disso, estudos com dados reais são apresentados em todos os artigos, nos quais são estimador rankings de eficiência para uma amostra de departamentos policiais dos EUA, a partir de dados sobre criminalidade daquele país. / There exists a large and growing literature on the specification and estimation of production frontiers and therefore efficiency of production units. In this thesis we focus on deterministic production frontier models, which are based on the assumption that all observed data lie in the technological set. Among the existing statistical models and estimators for deterministic frontiers, a promising approach is that of Martins-Filho and Yao (2007). They propose an estimation procedure that consists of three stages. Their estimator is fairly easy to implement as it involves standard nonparametric procedures. In addition, it has a number of desirable characteristics vis-a-vis traditional deterministic frontier estimators as DEA and FDH. In this thesis we propose three papers that improve the model proposed in Martins-Filho and Yao (2007). In the first paper we improve their estimation procedure by adopting a variant of the local exponential smoothing proposed in Ziegelmann (2002). Our estimator is shown to be consistent and asymptotically normal. In addition, due to local exponential smoothing, potential negativity of conditional variance functions that may hinder the use of Martins-Filho and Yao's estimator is avoided. In the second paper we propose a novel method for estimating production frontiers in only two stages. (Continue). There we show that we can eliminate the second stage of Martins-Filho and Yao as well as of our first paper, where estimation of the same frontier model requires three stages under different versions for the second stage. We study asymptotic properties showing consistency andNirtnin, asymptotic normality of our proposed estimator under standard assumptions. In the third paper we propose a semiparametric variation of the frontier model studied in the second paper. We rewrite that model allowing for estimating the production frontier and efficiency of production units in a multiple input context without suffering the curse of dimensionality. Our approach places that model within the framework of additive models based on assumptions regarding the way inputs combine in production. In particular, we consider the cases of additive and multiplicative inputs, which are widely considered in economic theory and applications. Monte Carlo studies are performed in all papers to shed light on the finite sample properties of the proposed estimators. Furthermore a real data study is carried out in all papers, from which we rank efficiency within a sample of USA Law Enforcement agencies using USA crime data.

Existe uma grande e crescente literatura sobre especificação e estimação de fronteiras de produção e, portanto, de eficiência de unidades produtivas. Nesta tese, o foco esta sobre modelos de fronteiras determinísticas, os quais são baseados na hipótese de que os dados observados pertencem ao conjunto tecnológico. Dentre os modelos estatísticos e estimadores para fronteiras determinísticas existentes, uma abordagem promissora e a adotada por Martins-Filho e Yao (2007). Esses autores propõem um procedimento de estimação composto por três estágios. Esse estimador e de fácil implementação, visto que envolve procedimentos não-paramétricos bem conhecidos. Além disso, o estimador possui características desejáveis vis-à-vis estimadores para fronteiras determinísticas tradicionais como DEA e FDH. Nesta tese, três artigos, que melhoram o modelo proposto por Martins-Filho e Yao (2007), sao propostos. No primeiro artigo, o procedimento de estimação desses autores e melhorado a partir de uma variação do estimador exponencial local, proposto por Ziegelmann (2002). Demonstra-se que estimador proposto a consistente e assintoticamente normal. Além disso, devido ao estimador exponencial local, estimativas potencialmente negativas para a função de variância condicional, que poderiam prejudicar a aplicabilidade do estimador proposto por Martins-Filho e Yao, são evitadas. No segundo artigo, e proposto um método original para estimação de fronteiras de produção em apenas dois estágios. E mostrado que se pode eliminar o segundo estágio proposto por Martins-Filho e Yao, assim como, eliminar o segundo estagio proposto no primeiro artigo desta tese. Em ambos os casos, a estimação do mesmo modelo de fronteira de produção requer três estágios, sendo versões diferentes para o segundo estagio. As propriedades assintóticas do estimador proposto são analisadas, mostrando-se consistência e normalidade assintótica sob hipóteses razoáveis. No terceiro artigo, a proposta uma variação semi-paramétrica do modelo estudado no segundo artigo. Reescreve-se aquele modelo de modo que se possa estimar a fronteira de produção e a eficiência de unidades produtivas no contexto de múltiplos insumos, sem incorrer no curse of dimensionality. A abordagem adotada coloca o modelo na estrutura de modelos aditivos, a partir de hipóteses sobre como os insumos se combinam no processo produtivo. Em particular, considera-se aqui os casos de insumos aditivos e insumos multiplicativos, os quais são amplamente considerados em teoria econômica e aplicações. Estudos de Monte Carlo são apresentados em todos os artigos, afim de elucidar as propriedades dos estimadores propostos em amostras finitas. Além disso, estudos com dados reais são apresentados em todos os artigos, nos quais são estimador rankings de eficiência para uma amostra de departamentos policiais dos EUA, a partir de dados sobre criminalidade daquele país. / There exists a large and growing literature on the specification and estimation of production frontiers and therefore efficiency of production units. In this thesis we focus on deterministic production frontier models, which are based on the assumption that all observed data lie in the technological set. Among the existing statistical models and estimators for deterministic frontiers, a promising approach is that of Martins-Filho and Yao (2007). They propose an estimation procedure that consists of three stages. Their estimator is fairly easy to implement as it involves standard nonparametric procedures. In addition, it has a number of desirable characteristics vis-a-vis traditional deterministic frontier estimators as DEA and FDH. In this thesis we propose three papers that improve the model proposed in Martins-Filho and Yao (2007). In the first paper we improve their estimation procedure by adopting a variant of the local exponential smoothing proposed in Ziegelmann (2002). Our estimator is shown to be consistent and asymptotically normal. In addition, due to local exponential smoothing, potential negativity of conditional variance functions that may hinder the use of Martins-Filho and Yao's estimator is avoided. In the second paper we propose a novel method for estimating production frontiers in only two stages. (Continue). There we show that we can eliminate the second stage of Martins-Filho and Yao as well as of our first paper, where estimation of the same frontier model requires three stages under different versions for the second stage. We study asymptotic properties showing consistency andNirtnin, asymptotic normality of our proposed estimator under standard assumptions. In the third paper we propose a semiparametric variation of the frontier model studied in the second paper. We rewrite that model allowing for estimating the production frontier and efficiency of production units in a multiple input context without suffering the curse of dimensionality. Our approach places that model within the framework of additive models based on assumptions regarding the way inputs combine in production. In particular, we consider the cases of additive and multiplicative inputs, which are widely considered in economic theory and applications. Monte Carlo studies are performed in all papers to shed light on the finite sample properties of the proposed estimators. Furthermore a real data study is carried out in all papers, from which we rank efficiency within a sample of USA Law Enforcement agencies using USA crime data.