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當母體中有部份對象因被治癒或免疫而不會失敗時，需考慮這群對象所佔的比率，即存活分率。本文主要在探討如何以貝氏方法對含存活分率之治癒率模式進行分析，並特別針對兩種含存活分率的迴歸模式，分別是Weibull迴歸模式以及對數邏輯斯迴歸模式，導出概似函數與各參數之完全條件後驗分配及其性質。由於聯合後驗分配相當複雜，各參數之邊際後驗分配之解析形式很難表達出。所以，我們採用了馬可夫鏈蒙地卡羅方法（MCMC）中的Gibbs抽樣法及Metropolis法，模擬產生參數值，以進行貝氏分析。實證部份，我們分析了黑色素皮膚癌的資料，這是由美國Eastern Cooperative Oncology Group所進行的第三階段臨床試驗研究。有關模式選取的部份，我們先分別求出各對象在每個模式之下的條件預測指標（CPO），再據以算出各模式的對數擬邊際概似函數值（LPML），以比較各模式之適合性。 / When we face the problem that part of subjects have been cured or are immune so they never fail, we need to consider the fraction of this group among the whole population, which is the so called survival fraction. This article discuss that how to analyze cure rate models containing survival fraction based on Bayesian method. Two cure rate models containing survival fraction are focused; one is based on the Weibull regression model and the other is based on the log-logistic regression model. Then, we derive likelihood functions and full conditional posterior distributions under these two models. Since joint posterior distributions are both complicated, and marginal posterior distributions don’t have closed form, we take Gibbs sampling and Metropolis sampling of Markov Monte Carlo chain method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the data from a melanoma clinical trial in the third stage conducted by Eastern Cooperative Oncology Group. To do model selection, we compute the conditional predictive ordinate (CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudomarginal likelihood (LPML) of each model.

長期性資料(longitudinal data)的最主要特徵是為對多個被觀測個體在不同的時間點上重複測量一個或多個反應變數。而在分析長期性資料的方法中，Laird & Ware(1982)建議以線性混合效果模型(linear mixed effects model，LME)來進行估計分析，此模型方法中，資料可以允許遺失值，並可將受測個體間與個體內的變異分開說明。 另在配適最小平方法(OLS)的迴歸模型中，係數估計經常會受到異常值的影響，而Rousseeuw & Leroy(1987)提出最小消去平方法(least trimmed squares，LTS)的穩健迴歸模型，即是解決最小平方法中對於異常值敏感的問題。 本研究主要針對台灣股票預期報酬之三種模型：資本資產定價模型、特徵模型、因子模型分別以OLS、LTS、LME三種估計方法做配適，並比較配適模型之適當與否，樣本資料為民國七十年七月至九十年六月共252個月516家上市公司股票報酬。實證結果顯示，不論是採用OLS、LTS、LME的估計方法，股票報酬解釋變數：系統風險、公司規模、帳面權益對市值比、SMB、HML皆為股票報酬的顯著解釋因子；而在模型比較方面，不論是配適資本資產定價模型、特徵模型或因子模型，LME都較OLS為較適當配適模型。這顯示了在分析長期性資料時，LME的確是一個較佳的統計分析模型。

本文主要在探討自變數存在有測量誤差時，邏輯式迴歸模型的估計問題，並設計實驗使得測量誤差能滿足遞減假設，進一步應用序貫分析方法，在給定水準下，建立一個信賴範圍。 當自變數存在有測量誤差時，通常會得到有偏誤的估計量，進而在做決策時會得到與無測量誤差所做出的決策不同。在本文中提出了一個遞減的測量誤差，使得滿足這樣的假設，可以證明估計量的強收斂，並證明與無測量誤差所得到的估計量相同的近似分配。相較於先前的假設，特別是證明大樣本的性質，新增加的樣本會有更小的測量誤差是更加合理的假設。我們同時設計了一個實驗來滿足所提出遞減誤差的條件，並利用序貫設計得到一個更省時也節省成本的處理方法。 一般的case-control實驗，自變數也會出現測量誤差，我們也證明了斜率估計量的強收斂與近似分配的性質，並提出一個二階段抽樣方法，計算出所需的樣本數及建立信賴區間。 / In this thesis, we focus on the estimate of unknown parameters, experimental designs and sequential methods in both prospective and retrospective logistic regression models when there are covariates measured with errors. The imprecise measurement of exposure happens very often in practice, for example, in retrospective epidemiology studies, that may due to either the difficulty or the cost of measuring. It is known that the imprecisely measured variables can result in biased coefficients estimation in a regression model and therefore, it may lead to an incorrect inference. Thus, it is an important issue if the effects of the variables are of primary interest. When considering a prospective logistic regression model, we derive asymptotic results for the estimators of the regression parameters when there are mismeasured covariates. If the measurement error satisfies certain assumptions, we show that the estimators follow the normal distribution with zero mean, asymptotically unbiased and asymptotically normally distributed. Contrary to the traditional assumption on measurement error, which is mainly used for proving large sample properties, we assume that the measurement error decays gradually at a certain rate as there is a new observation added to the model. This kind of assumption can be fulfilled when the usual replicate observation method is used to dilute the magnitude of measurement errors, and therefore, is also more useful in practical viewpoint. Moreover, the independence of measurement error and covariate is not required in our theorems. An experimental design with measurement error satisfying the required degenerating rate is introduced. In addition, this assumption allows us to employ sequential sampling, which is popular in clinical trials, to such a measurement error logistic regression model. It is clear that the sequential method cannot be applied based on the assumption that the measurement errors decay uniformly as sample size increasing as in the most of the literature. Therefore, a sequential estimation procedure based on MLEs and such moment conditions is proposed and can be shown to be asymptotical consistent and efficient. Case-control studies are broadly used in clinical trials and epidemiological studies. It can be showed that the odds ratio can be consistently estimated with some exposure variables based on logistic models (see Prentice and Pyke (1979)). The two-stage case-control sampling scheme is employed for a confidence region of slope coefficient beta. A necessary sample size is calculated by a given pre-determined level. Furthermore, we consider the measurement error in the covariates of a case-control retrospective logistic regression model. We also derive some asymptotic results of the maximum likelihood estimators (MLEs) of the regression coefficients under some moment conditions on measurement errors. Under such kinds of moment conditions of measurement errors, the MLEs can be shown to be strongly consistent, asymptotically unbiased and asymptotically normally distributed. Some simulation results of the proposed two-stage procedures are obtained. We also give some numerical studies and real data to verify the theoretical results in different measurement error scenarios.

La question de la transmission internationale des cycles a reçu une attention considérable en raison de l’intensification de la globalisation économique et financière. La problématique générale de cette thèse s’inscrit dans le prolongement de la littérature consacrée à cette question. Plus précisément, elle focalise son attention sur l’analyse de la transmission du cycle des Etats-Unis sur les pays émergents. Elle comporte trois chapitres. Le premier, en se basant sur une nouvelle approche économétrique en termes de modèle Global VAR, s’attache à étudier l’effet des chocs provenant des Etats-Unis sur les pays émergents. Il confirme l’idée que les Etats-Unis jouent un rôle important dans la transmission des cycles économiques étant donné leur poids dans l’économie mondiale. Le second chapitre propose d’étudier la transmission financière des Etats-Unis en s’intéressant à la crise des subprimes sur ces pays. L’estimation du modèle switch à probabilité variée développée indique que la persistance des stress financiers, le durcissement des conditions du crédit et l’augmentation du risque de non-solvabilité bancaire ont été les causes fondamentales de la transmission financière. La volatilité de l’indice boursier américain a été le facteur clé de la contamination avec tous les pays étudiés. Le troisième chapitre est consacré à étudier si les pays émergents sont en mesure d’adopter des politiques budgétaires contracycliques pouvant atténuer les chocs provenant de l’extérieur. En utilisant le modèle à seuil avec transition lisse en panel (le modèle PSTR), ce chapitre confirme que la politique budgétaire dans les pays émergents est procyclique en période de ralentissement économique et aussi lorsque la dette publique dépasse le seuil critique. De ce fait, une solide position budgétaire est fondamentale pour assurer la stabilité macroéconomique. / The issue of international transmission cycles has considerably received attention due to the increasing economic and financial globalization. Our thesis is in line with the literature dedicated to this question. More specifically, we focusour attention on the analysis of the transmission cycle of the United States to emerging countries. It consists of three chapters. The first one, based on a new econometric approach in terms of Global VAR model, aims to study the effect of shocks from the U.S. to emerging countries. The main resultconfirms the idea that the United States plays an important role in the transmission of economic cycles given their weight in the world economy. The second chapter proposes to study the financial transmission of the United States by focusing on the subprime crisis on these countries. The estimation of time varyingtransitionprobability (TVTP) Markov switchingmodel indicates that the persistence of financial stress, the tightening of the conditions of the credit and the increase of the risk of Banking solvency constitute the major determinants of the financial transmission. The US stock market volatility is the key factor transmission channel for all the studied countries. The third chapter is devoted to investigate whether emerging countries are able to adopt countercyclical fiscal policies to mitigate the impact from outside. Using the threshold model with smooth transition panel ( the PSTR model ), this chapter confirms that fiscal policy in emerging countries is procyclicalin the slowdown periodand also when public debt exceeds the critical threshold. Therefore, a strong fiscal position is fundamental to ensure macroeconomic stability.

Propor uma família de distribuição de probabilidade mais ampla e flexível é de grande importância em estudos estatísticos. Neste trabalho é utilizado um novo método de adicionar um parâmetro para uma distribuição contínua. A distribuição gama generalizada, que tem como casos especiais a distribuição Weibull, exponencial, gama, qui-quadrado, é usada como distribuição base. O novo modelo obtido tem quatro parâmetros e é chamado odd log-logística gama generalizada (OLLGG). Uma das características interessante do modelo OLLGG é o fato de apresentar bimodalidade. Outra proposta deste trabalho é introduzir um modelo de regressão chamado log-odd log-logística gama generalizada (LOLLGG) com base na GG (Stacy e Mihram, 1965). Este modelo pode ser muito útil, quando por exemplo, os dados amostrados possuem uma mistura de duas populações estatísticas. Outra vantagem da distribuição OLLGG consiste na capacidade de apresentar várias formas para a função de risco, crescente, decrescente, na forma de U e bimodal entre outras. Desta forma, são apresentadas em ambos os casos as expressões explícitas para os momentos, função geradora e desvios médios. Considerando dados nãocensurados e censurados de forma aleatória, as estimativas para os parâmetros de interesse, foram obtidas via método da máxima verossimilhança. Estudos de simulação, considerando diferentes valores para os parâmetros, porcentagens de censura e tamanhos amostrais foram conduzidos com o objetivo de verificar a flexibilidade da distribuição e a adequabilidade dos resíduos no modelo de regressão. Para ilustrar, são realizadas aplicações em conjuntos de dados reais. / Providing a wider and more flexible probability distribution family is of great importance in statistical studies. In this work a new method of adding a parameter to a continuous distribution is used. In this study the generalized gamma distribution (GG) is used as base distribution. The GG distribution has, as especial cases, Weibull distribution, exponential, gamma, chi-square, among others. For this motive, it is considered a flexible distribution in data modeling procedures. The new model obtained with four parameters is called log-odd log-logistic generalized gamma (OLLGG). One of the interesting characteristics of the OLLGG model is the fact that it presents bimodality. In addition, a regression model regression model called log-odd log-logistic generalized gamma (LOLLGG) based by GG (Stacy e Mihram, 1965) is introduced. This model can be very useful when, the sampled data has a mixture of two statistical populations. Another advantage of the OLLGG distribution is the ability to present various forms for the failing rate, as increasing, as decreasing, and the shapes of bathtub or U. Explicity expressions for the moments, generating functions, mean deviations are obtained. Considering non-censored and randomly censored data, the estimates for the parameters of interest were obtained using the maximum likelihood method. Simulation studies, considering different values for the parameters, percentages of censoring and sample sizes were done in order to verify the distribuition flexibility, and the residues distrbutuon in the regression model. To illustrate, some applications using real data sets are carried out.

Climate change implication and rural livelihood capitals remain the major inextricable dimensions of sustainability in this twenty first century globally. As a result, the impact and outcome of climate change on rural livelihood capitals, including economic development cannot be overemphasized in Ngaka Modiri Molema District Municipality of the North West Province of South Africa, where the study took place. It is one of the largest maize production regions in South Africa, where a preponderance of the people in the province obtain their livelihood from agriculture which contributes enormously to the promotion of household’s food security. The study, therefore, investigated the adaptation strategies, awareness of climate change, factors that influenced climate change adaptation in North West Province of South Africa, with the aim of ascertaining the effects of climate change on livelihood capitals among small and emerging maize farmers. Stratified random sampling technique was used to select three hundred and forty-six (346) farmers who were interviewed from the study area, while a pre-tested questionnaire was administered to the maize farmers, aiming at matters related to climate change impact on livelihood and adaptation. Data were analyzed using descriptive statistics while inferential statistical tools employed were Principal Component Analysis, Two-Stage Least Square regression model, Binary Logistic regression model, and Tobit regression model. The results of the study showed that climate change was linked to rural livelihood capitals as climate change awareness, low profit and co-operative finance were statistically significant (p<0.05). The study also established that majority of the rural farmers in the study area were aware of climate change, in which farm size, education, ownership of the farm, information received on climate change, source of climate change information, climate change information through extension services, channel of information received on climate change and support received on climate change were statistically significant (p<0.05). Factors such as farm size, household gender, type of farms, who owns the farm, land acquisition, source of climate change information, support received on climate change, and adaptation barrier were statistically significant (p<0.05) and influenced climate change adaptation in the study area. Conclusively, climate change is entwined with rural livelihood, and the variables that are significant to the study were identified. It was therefore recommended that government intervention, access to information, extension service and support, farmers’ networking, adoption of drought and heat stress tolerant seeds, indigenous knowledge should be improved, practiced and promoted among the rural farmers and the stakeholders involved in the study area. / Agriculture, Animal Health and Human Ecology / D. Phil. (Agriculture)

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本篇論文主要考慮成群資料的存活分析，其特點為群內個體間具有相關性，並假定群內個體具有相同但無法觀測到的事故傾向。首先，探討事故傾向服從任一連續分配時混合Weibull迴歸模式的特性，接著，推導出事故傾向服從血Inverse Gaussian吧時之混合Weibull模式，並介紹參數的估計問題。然後，推導出群內個體是否獨立之分數檢定統計量，以分別就兩種最常見的存活資料型態一完整型態與右設限型態：檢定模式中事故傾向的效應是否存在。最後，並以實例說明分數檢定之程序。 / In this paper, we study survival analysis for grouped data, where the within group correlations are considered. It is also assumed that individuals within the same group share a common but unobservable random frailty. First, we discuss the properties of the Weibull regression model mixed by any continuous distribution. Next, we derive an Inverse Gaussan mixture of Weibull regression model, and discuss the estimation problem. Then, we derive the score test for testing independence between components within the same group, where the two most common cases are discussed the complete data case and the right censoring case. Finally, the testing procedures are illustrated by two examples.

本研究試圖瞭解投資人所關心的財務資訊，是否真能帶來超額報酬，亦即探討上市公司股票報酬率與各財務資訊之間的關係，包括每股盈餘成長率及益本比、市價淨值比、自由現金流量相關變數對長期股票報酬之影響，並嘗試對各變數給予經濟上的解釋。 　　其中並試圖找出財務資訊究竟是在何時反應於股票報酬與超額報酬上，因此將股票報酬與超額報酬以領先財務資訊一季、與財務資訊同季及落後財務資訊一季等三個時點加以衡量，並以表面無關迴歸模式(Seemingly Unrelated Regression model ; SUR)與混合橫斷面及縱斷面之迴歸模式進行統計分析。 　　結果發現益本比及每股盈餘成長率與股票報酬及超額報酬的關係並不顯著；市價淨值比與落後一季的股價報酬具有顯著的負相關，而與超額報酬不論衡量時點為何均存在有顯著正相關；自由現金流量與股價報酬及額報酬均無顯著關係；毛現金流量與經濟利益率與股價報酬在部分產業中具有顯著關係，而與當期超額股價報酬則存在顯著的關係，惟影響符號不一致。此外各自變數對於股票超額報酬的關連性較自變數與股票報酬間具有較顯著的關係。