In analysis of the contingency tables, the Fisher's exact test is a very important statistical significant test that is commonly used to test independence between the two variables. However, the Fisher' s exact test is based upon the assumption of the fixed margins. That is, the Fisher's exact test uses information beyond the table so that it is conservative. To solve this problem, we allow the margins to be random. This means that instead of fitting the count data to the hypergeometric distribution as in the Fisher's exact test, we model the margins and one cell using multinomial distribution, and then we use the likelihood ratio to test the hypothesis of independence. Furthermore, using Bayesian inference, we consider the Bayes factor as another test statistic. In order to judge the test performance, we compare the power of the likelihood ratio test, the Bayes factor test and the Fisher's exact test. In addition, we use our methodology to analyse data gathered from the Worcester Heart Attack Study to assess gender difference in the therapeutic management of patients with acute myocardial infarction (AMI) by selected demographic and clinical characteristics.

Under the mechanism of natural selection, creatures are forced to evolve naturally in order to survive. Keen-sighted jumping spiders have long been considered as the main predation pressure of terrestrial arthropod. Many species benefit from mimicking the appearance of jumping spider. In this study according to the experimental data from Wang (2009b), a data analysis is undertaken concerning male Ptocasius strupifer¡¦s behavior to different subject groups, namely, male Ptocasius strupifer, female Ptocasius strupifer, male Plexippus paykulli, female Plexippus paykulli, Cataclysta angulata and Eugauria albidentata, so as to investigate the jumping spider mimicry of Eugauria albidentata. In this work, our interest is to compare the behavior of male Ptocasius strupifer on Eugauria albidentata with there of the other five groups mentioned above, and identify which one is the most similar to there of Eugauria albidentata . We use different statistical methods, i.e. likelihood ratio test, factor analysis and cluster analysis to evaluate the closeness of the behavior between different groups. According to the analysis result, it shows that the behavior of Ptocasius strupifer towards Eugauria albidentata is more similar to those of both female Ptocasius strupifer and female Plexippus paykulli. Moreover there is a wide discrepancy between Eugauria albidentata and Cataclysta angulata, although both of them belong to Musotiminae.

Given the ever-growing demand for radio spectrum, cognitive radio has recently emerged as an attractive wireless communication technology. This dissertation is concerned with developing spectrum sensing algorithms in cognitive radio networks where a single or multiple cognitive radios (CRs) assist in detecting licensed primary bands employed by single or multiple primary users. First, given that orthogonal frequency-division multiplexing (OFDM) is an important wideband transmission technique, detection of OFDM signals in low-signal-to-noise-ratio scenario is studied. It is shown that the cyclic prefix correlation coefficient (CPCC)-based spectrum sensing algorithm, which was previously introduced as a simple and computationally efficient spectrum-sensing method for OFDM signals, is a special case of the constrained generalized likelihood ratio test (GLRT) in the absence of multipath. The performance of the CPCC-based algorithm degrades in a multipath scenario. However when OFDM is implemented, by employing the inherent structure of OFDM signals and exploiting multipath correlation in the GLRT algorithm a simple and low-complexity algorithm called the multipath-based constrained-GLRT (MP-based C-GLRT) algorithm is obtained. Further performance improvement is achieved by combining both the CPCC- and MP-based C-GLRT algorithms. A simple GLRT-based detection algorithm is also developed for unsynchronized OFDM signals. In the next part of the dissertation, a cognitive radio network model with multiple CRs is considered in order to investigate the benefit of collaboration and diversity in improving the overall sensing performance. Specially, the problem of decision fusion for cooperative spectrum sensing is studied when fading channels are present between the CRs and the fusion center (FC). Noncoherent transmission schemes with on-off keying (OOK) and binary frequency-shift keying (BFSK) are employed to transmit the binary decisions to the FC. The aim is to maximize the achievable secondary throughput of the CR network. Finally, in order to reduce the required transmission bandwidth in the reporting phase of the CRs in a cooperative sensing scheme, the last part of the dissertation examines nonorthogonal transmission of local decisions by means of on-off keying. Proposed and analyzed is a novel decoding-based fusion rule for combining the hard decisions in a linear manner.

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O cenário agrícola nacional tem se tornado cada vez mais competitivo ao longo dos anos, manter o crescimento da produtividade a um baixo custo operacional e com baixo impacto ambiental tem sido os três ingredientes de maior relevância na área. A produtividade por sua vez, é função de várias variáveis, sendo o controle de plantas daninhas uma dessas variáveis a ser considerada. Nesse trabalho é analisado um conjunto de dados de um experimento realizado no departamento de Produção Vegetal da ESALQ-USP, Piracicaba - SP. Foram avaliadas 4 biótipos de capim-pé-de-galinha provenientes de três estados brasileiros e em três estágios morfológicos com 4 repetições para cada biótipo, a variável resposta utilizada foi massa seca (g) e como variável regressora foi utilizada a dose de glyphosate nas concentrações variando de 1/16 D a 16 D mais a testemunha, sem aplicação de herbicida, em que D varia de 480 gramas de equivalente ácido de glyphosate por hectare (g .e a. ha-1) para o estágio de 2 a 3 perfilhos, 720 (g .e a. ha-1) para o estágio de 6 a 8 perfilhos e de 960 para o estágio de 10-12 perfilhos. O trabalho teve como objetivo primário avaliar se, ao longo dos anos, as populações de capim-pé-de-galinha tem se tornado resistentes ao herbicida glyphosate, visando detecção de biótipos resistentes. O experimento foi instalado segundo o delineamento inteiramente aleatorizado, sendo feito em três estágios diferentes. Para a análise dos dados foi utilizado o modelo não-linear log-logístico proposto em Knezevic, S. e Ritz (2007) como método univariado, foi utilizado ainda o método da máxima verossimilhança para verificar a igualdade do parâmetro e. O modelo utilizado convergiu para quase todas as repetições, mas não houve um comportamento sistemático observado que explicasse a não convergência de uma repetição em particular. Num segundo momento, as estimativas dos três parâmetros do modelo foram tomadas como variáveis dependentes em uma análise de variância multivariada. Observando que as três, conjuntamente, foram significativas pelos testes de Pillai, Wilks, Roy e Hotelling-Lawley, foi realizado o teste de Tukey para o mesmo parâmetro e comparado com o primeiro método utilizado. Esse procedimento apresentou, com o mesmo coeficiente de significância, menor capacidade de identificar diferença entre as médias dos parâmetros das variedades de capim do que o método proposto por Regazzi (2015). / The national agricultural scenery has become increasingly competitive over the years, maintaining productivity growth at a low operating cost and low environmental impact has been the three most important ingredients in the area. Productivity in turn is a function of several variables, and the weed control is one of these variables to be considered. In this work it is analyzed a dataset of an experiment conducted in the Plant Production Department of ESALQ-USP, Piracicaba - SP. Were evaluated 4 grass chicken\'s feet biotypes from three Brazilian states in three morphological stages with 4 repetitions for each biotype, the response variable used was dry mass (g) and as regressor variable were used the dose of glyphosate in concentrations ranging from 1/16 D to 16 D plus the control without herbicide, wherein D ranges from 480 grams of glyphosate acid equivalent per hectare (g .e a. ha-1) for 2 to 3 stage tillers, 720 grams of glyphosate acid equivalent per hectare (g .e a. ha-1) for 6 to 8 tillers and 960 for stage 10-12 tillers. The work had as main objective to evaluate , if over the years, populations of grass chicken\'s feet has become resistant to glyphosate, aiming detection of resistant biotypes. The experiment was conducted under completely randomized design being done in three stages. For data analysis was used the non-linear log-logistic proposed in Knezevic, S. e Ritz (2007) as univariate method, it was still used the maximum likelihood method to verify the equality of the parameter e. The model converged to almost all repetitions, but there was an observed systematic behavior to explain the non-convergence of a particular repetition. Secondly, estimates of the three model parameters were taken as dependent variables in a multivariate analysis of variance. Noting that all three together, were significant by Pillai, Wilks, Roy and Hotelling-Lawley tests, was performed Tukey test for the same parameter e and compared with the first method. This procedure presented, with the same coefficient of significance, less able to identify differences between the means of the parameters of grass varieties than the method proposed by Regazzi (2015).

Regression analysis is one of the most applied statistical techniques. The sta- tistical inference of a linear regression model with a monotone constraint had been discussed in early analysis. A natural question arises when it comes to the difference between the cases of with and without the constraint. Although the comparison be- tween confidence intervals of linear regression models with and without restriction for one predictor variable had been considered, this discussion for multiple regres- sion is required. In this thesis, I discuss the comparison of the confidence intervals between a multiple linear regression model with and without constraints.

Regression analyses constitutes an important part of the statistical inference and has great applications in many areas. In some applications, we strongly believe that the regression function changes monotonically with some or all of the predictor variables in a region of interest. Deriving analyses under such constraints will be an enormous task. In this work, the restricted prediction interval for the mean of the regression function is constructed when two predictors are present. I use a modified likelihood ratio test (LRT) to construct prediction intervals.

O cenário agrícola nacional tem se tornado cada vez mais competitivo ao longo dos anos, manter o crescimento da produtividade a um baixo custo operacional e com baixo impacto ambiental tem sido os três ingredientes de maior relevância na área. A produtividade por sua vez, é função de várias variáveis, sendo o controle de plantas daninhas uma dessas variáveis a ser considerada. Nesse trabalho é analisado um conjunto de dados de um experimento realizado no departamento de Produção Vegetal da ESALQ-USP, Piracicaba - SP. Foram avaliadas 4 biótipos de capim-pé-de-galinha provenientes de três estados brasileiros e em três estágios morfológicos com 4 repetições para cada biótipo, a variável resposta utilizada foi massa seca (g) e como variável regressora foi utilizada a dose de glyphosate nas concentrações variando de 1/16 D a 16 D mais a testemunha, sem aplicação de herbicida, em que D varia de 480 gramas de equivalente ácido de glyphosate por hectare (g .e a. ha-1) para o estágio de 2 a 3 perfilhos, 720 (g .e a. ha-1) para o estágio de 6 a 8 perfilhos e de 960 para o estágio de 10-12 perfilhos. O trabalho teve como objetivo primário avaliar se, ao longo dos anos, as populações de capim-pé-de-galinha tem se tornado resistentes ao herbicida glyphosate, visando detecção de biótipos resistentes. O experimento foi instalado segundo o delineamento inteiramente aleatorizado, sendo feito em três estágios diferentes. Para a análise dos dados foi utilizado o modelo não-linear log-logístico proposto em Knezevic, S. e Ritz (2007) como método univariado, foi utilizado ainda o método da máxima verossimilhança para verificar a igualdade do parâmetro e. O modelo utilizado convergiu para quase todas as repetições, mas não houve um comportamento sistemático observado que explicasse a não convergência de uma repetição em particular. Num segundo momento, as estimativas dos três parâmetros do modelo foram tomadas como variáveis dependentes em uma análise de variância multivariada. Observando que as três, conjuntamente, foram significativas pelos testes de Pillai, Wilks, Roy e Hotelling-Lawley, foi realizado o teste de Tukey para o mesmo parâmetro e comparado com o primeiro método utilizado. Esse procedimento apresentou, com o mesmo coeficiente de significância, menor capacidade de identificar diferença entre as médias dos parâmetros das variedades de capim do que o método proposto por Regazzi (2015). / The national agricultural scenery has become increasingly competitive over the years, maintaining productivity growth at a low operating cost and low environmental impact has been the three most important ingredients in the area. Productivity in turn is a function of several variables, and the weed control is one of these variables to be considered. In this work it is analyzed a dataset of an experiment conducted in the Plant Production Department of ESALQ-USP, Piracicaba - SP. Were evaluated 4 grass chicken\'s feet biotypes from three Brazilian states in three morphological stages with 4 repetitions for each biotype, the response variable used was dry mass (g) and as regressor variable were used the dose of glyphosate in concentrations ranging from 1/16 D to 16 D plus the control without herbicide, wherein D ranges from 480 grams of glyphosate acid equivalent per hectare (g .e a. ha-1) for 2 to 3 stage tillers, 720 grams of glyphosate acid equivalent per hectare (g .e a. ha-1) for 6 to 8 tillers and 960 for stage 10-12 tillers. The work had as main objective to evaluate , if over the years, populations of grass chicken\'s feet has become resistant to glyphosate, aiming detection of resistant biotypes. The experiment was conducted under completely randomized design being done in three stages. For data analysis was used the non-linear log-logistic proposed in Knezevic, S. e Ritz (2007) as univariate method, it was still used the maximum likelihood method to verify the equality of the parameter e. The model converged to almost all repetitions, but there was an observed systematic behavior to explain the non-convergence of a particular repetition. Secondly, estimates of the three model parameters were taken as dependent variables in a multivariate analysis of variance. Noting that all three together, were significant by Pillai, Wilks, Roy and Hotelling-Lawley tests, was performed Tukey test for the same parameter e and compared with the first method. This procedure presented, with the same coefficient of significance, less able to identify differences between the means of the parameters of grass varieties than the method proposed by Regazzi (2015).

This research study is the result of a 3 years CIFRE PhD thesis between the Airbus design office(Aircraft Control domain) and TéSA laboratory in Toulouse. The main goal is to propose, developand validate a software solution for the detection and diagnosis of a specific type of elevator andrudder vibration, called limit cycle oscillation (LCO), based on existing signals available in flightcontrol computers on board in-series aircraft. LCO is a generic mathematical term defining aninitial condition-independent periodic mode occurring in nonconservative nonlinear systems. Thisstudy focuses on the LCO phenomenon induced by mechanical freeplays in the control surface ofa civil aircraft. The LCO consequences are local structural load augmentation, flight handlingqualities deterioration, actuator operational life reduction, cockpit and cabin comfort deteriorationand maintenance cost augmentation. The state-of-the-art for freeplay induced LCO detection anddiagnosis is based on the pilot sensitivity to vibration and to periodic freeplay check on the controlsurfaces. This study is thought to propose a data-driven solution to help LCO and freeplaydiagnosis. The goal is to improve even more aircraft availability and reduce the maintenance costsby providing to the airlines a condition monitoring signal for LCO and freeplays. For this reason,two algorithmic solutions for vibration and freeplay diagnosis are investigated in this PhD thesis. Areal time detector for LCO diagnosis is first proposed based on the theory of the generalized likeli hood ratio test (GLRT). Some variants and simplifications are also proposed to be compliantwith the industrial constraints. In a second part of this work, a mechanical freeplay detector isintroduced based on the theory of Wiener model identification. Parametric (maximum likelihoodestimator) and non parametric (kernel regression) approaches are investigated, as well as somevariants to well-known nonparametric methods. In particular, the problem of hysteresis cycleestimation (as the output nonlinearity of a Wiener model) is tackled. Moreover, the constrainedand unconstrained problems are studied. A theoretical, numerical (simulator) and experimental(flight data and laboratory) analysis is carried out to investigate the performance of the proposeddetectors and to identify limitations and industrial feasibility. The obtained numerical andexperimental results confirm that the proposed GLR test (and its variants/simplifications) is a very appealing method for LCO diagnostic in terms of performance, robustness and computationalcost. On the other hand, the proposed freeplay diagnostic algorithm is able to detect relativelylarge freeplay levels, but it does not provide consistent results for relatively small freeplay levels. Moreover, specific input types are needed to guarantee repetitive and consistent results. Further studies should be carried out in order to compare the GLRT results with a Bayesian approach and to investigate more deeply the possibilities and limitations of the proposed parametric method for Wiener model identification.

We provide ways to test the fit of a parametric copula family for bivariate censored data with or without covariates. The proposed copula family is tested by embedding it in an expanded parametric family of copulas. When parameters in the proposed and the expanded copula models are estimated by maximum likelihood, a likelihood ratio test can be used. However, when they are estimated by two-stage pseudolikelihood estimation, the corresponding test is a pseudolikelihood ratio test. The two-stage procedures offer less computation, which is especially attractive when the marginal lifetime distributions are specified nonparametrically or semiparametrically. It is shown that the likelihood ratio test is consistent even when the expanded model is misspecified. Power comparisons of the likelihood ratio and the pseudolikelihood ratio tests with some other goodness-of-fit tests are performed both when the expanded family is correct and when it is misspecified. They indicate that model expansion provides a convenient, powerful and robust approach. We introduce a semiparametric maximum likelihood estimation method in which the copula parameter is estimated without assumptions on the marginal distributions. This method and the two-stage semiparametric estimation method suggested by Shih and Louis (1995) are generalized to regression models with Cox proportional hazards margins. The two-stage semiparametric estimator of the copula parameter is found to be about as good as the semiparametric maximum likelihood estimator. Semiparametric likelihood ratio and pseudolikelihood ratio tests are considered to provide goodness of fit tests for a copula model without making parametric assumptions for the marginal distributions. Both when the expanded family is correct and when it is misspecified, the semiparametric pseudolikelihood ratio test is almost as powerful as the parametric likelihood ratio and pseudolikelihood ratio tests while achieving robustness to the form of the marginal distributions. The methods are illustrated on applications in medicine and insurance. Sequentially observed survival times are of interest in many studies but there are difficulties in modeling and analyzing such data. First, when the duration of followup is limited and the times for a given individual are not independent, the problem of induced dependent censoring arises for the second and subsequent survival times. Non-identifiability of the marginal survival distributions for second and later times is another issue, since they are observable only if preceding survival times for an individual are uncensored. In addition, in some studies, a significant proportion of individuals may never have the first event. Fully parametric models can deal with these features, but lack of robustness is a concern, and methods of assessing fit are lacking. We introduce an approach to address these issues. We model the joint distribution of the successive survival times by using copula functions, and provide semiparametric estimation procedures in which copula parameters are estimated without parametric assumptions on the marginal distributions. The performance of semiparametric estimation methods is compared with some other estimation methods in simulation studies and shown to be good. The methodology is applied to a motivating example involving relapse and survival following colon cancer treatment.