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71	Efron’s Method on Large Scale Correlated Data and Its Refinements Ghoshal, Asmita 11 August 2023 (has links) No description available. Statistics Simultaneous Hypothesis Testing Large Scale Analysis Step-Wise Procedures False Discovery Rate (FDR) Family Wise Error Rate(FWER) Holm's Step-Down Procedure Refined Step-Down Algorithm Bootstrap Simultaneous Confidence Interval Contingency Table Strata Chi-Square Test Cochran-Mantel-Haenszel test Nonparametric Tests 2-sample t-test
72	Application Of The Empirical Likelihood Method In Proportional Hazards Model He, Bin 01 January 2006 (has links) In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) approach to construct goodness-of-fit test and provide estimates for the Cox model with various types of censored data. Specifically, the problems under consideration are the two-sample Cox model and stratified Cox model with right censored data, doubly censored data and partly interval-censored data. Related computational issues are discussed, and some simulation results are presented. The procedures developed in the work are applied to several real data sets with some discussion. Dissertations Academic -- Sciences Sciences -- Dissertations Academic Statistical hypothesis testing Survival analysis (Biometry) Bootstrap Confidence interval Cox model Doubly censored data Empirical likelihood function Goodness of fit test Maximum likelihood Partly interval censored data Proportional hazards model Right censored data Survival analysis Mathematics
73	Some Contributions to Inferential Issues of Censored Exponential Failure Data Han, Donghoon 06 1900 (has links) In this thesis, we investigate several inferential issues regarding the lifetime data from exponential distribution under different censoring schemes. For reasons of time constraint and cost reduction, censored sampling is commonly employed in practice, especially in reliability engineering. Among various censoring schemes, progressive Type-I censoring provides not only the practical advantage of known termination time but also greater flexibility to the experimenter in the design stage by allowing for the removal of test units at non-terminal time points. Hence, we first consider the inference for a progressively Type-I censored life-testing experiment with k uniformly spaced intervals. For small to moderate sample sizes, a practical modification is proposed to the censoring scheme in order to guarantee a feasible life-test under progressive Type-I censoring. Under this setup, we obtain the maximum likelihood estimator (MLE) of the unknown mean parameter and derive the exact sampling distribution of the MLE through the use of conditional moment generating function under the condition that the existence of the MLE is ensured. Using the exact distribution of the MLE as well as its asymptotic distribution and the parametric bootstrap method, we discuss the construction of confidence intervals for the mean parameter and their performance is then assessed through Monte Carlo simulations. Next, we consider a special class of accelerated life tests, known as step-stress tests in reliability testing. In a step-stress test, the stress levels increase discretely at pre-fixed time points and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Here, we consider a k-step-stress accelerated life testing experiment with an equal step duration τ. In particular, the case of progressively Type-I censored data with a single stress variable is investigated. For small to moderate sample sizes, we introduce another practical modification to the model for a feasible k-step-stress test under progressive censoring, and the optimal τ is searched using the modified model. Next, we seek the optimal τ under the condition that the step-stress test proceeds to the k-th stress level, and the efficiency of this conditional inference is compared to the preceding models. In all cases, censoring is allowed at each change stress point iτ, i = 1, 2, ... , k, and the problem of selecting the optimal Tis discussed using C-optimality, D-optimality, and A-optimality criteria. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. Thus, we also consider the simple stepstress models under Type-I and Type-II censoring situations when the lifetime distributions corresponding to the different risk factors are independently exponentially distributed. Under this setup, we derive the MLEs of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and then assess their performance through Monte Carlo simulations. / Thesis / Doctor of Philosophy (PhD) A-optimality accelerated life-testing C-optimality change point competing risks conditional inference conditional moment generating function confidence interval cumulative exposure model D-optimality exponential distribution maximum likelihood estimation order statistics parametric boootstrap method progressive Type-I censoring step-stress model tail probability Type-1 censoring Type-II censoring
74	壽險公司責任準備金涉險值之估計 / The Estimation of Value at Risk for the Reserve of Life/Health Insurance Company 詹志清, Chihching Chan Unknown Date (has links) 中文摘要在本文中，我們依據模擬的風險因子變動，包括死亡率風險，利率風險，解約率風險以及模型的參數風險，來估計第一個保單年度的期末責任準備金之涉險值 (Value at Risk)。本文中，雖僅計算生死合險保單的準備金之涉險值，但是本文所提供的方法以及計算過程可以很容易的應用到其它險種，甚至配合資產面的考量來計算保險公司盈餘(Surplus)的涉險值，進而作為清償能力的監測系統。本文的特點包括下列幾項：第一，本文提供了一個不同於傳統短期間(Short Horizon)的涉險值計算方式，來估計壽險商品的保單責任準備金(Policy Reserve)的涉險值。第二，本文利用生命表來估計死亡率風險所造成的涉險值。第三，我們利用隨機利率模型來捕捉隨機利率對於責任準備金涉險值的影響。第四，我們考慮解約率對於責任準備金涉險值的影響，值得注意的是，在我們的解約率模型中，引入的利率對於解約率的影響。第五，本文亦考慮風險因子模型當中的參數風險對於涉險值的影響。最後，我們利用無母數方法計算出涉險值的信賴區間，而信賴區間的估計在模擬過程當中尤其重要，因為它可以用來決定模擬次數的多寡。本文包含六節：第一節為導論。第二節為計算死亡率風險的責任準備金涉險值。第三節是計算加上利率風險後責任準備金涉險值的變化。第四節則為加上解約率後對涉險值的影響。第五節為計算涉險值的信賴區間。第六節是我們的結論以及後續研究的方向探討。本文包含六節：第一節為導論。第二節為計算死亡率風險的責任準備金涉險值。第三節是計算加上利率風險後責任準備金涉險值的變化。第四節則為加上解約率後對涉險值的影響。第五節為計算涉險值的信賴區間。第六節是我們的結論以及後續研究的方向探討。 / ABSTRACT In this paper, we estimate the VAR of life insurer's terminal reserve of the first policy year by the simulated risk factors, including mortality risk, interest rate risk, lapse rate risk, and estimation risks, of future twenty years. We found that the difference between the VAR under the mortality risk and the interest rate risk is very large because interest rate is a stochastic process but not mortality rate. Thus, the dispersion of interest rate is more then mortality rate. In addition, the VAR will reduce a lot after adding the impact of lapses because the duration of the reserve reduced. If we neglect the impact of lapses to VAR, we will overestimate the VAR significantly. The features of this paper are as follows. First, we provide an approach to measure the VAR of a life insurer's reserve, and it is rather different from traditional VAR with short horizons. Second, we use mortality table to estimate the VAR of a life insurer's reserve. Third, we use stochastic interest rate model to capture the effect of random interest rate to the VAR of a life insurer's reserve. Fourth, we relate the future cash outflows to interest rate and produce a reasonable estimator of VAR. Fifth, we consider the effect of estimation errors to the VAR of a life insurer's reserve. Last, we calculate the confidence interval of the VAR estimates of the policy reserves. This paper consists of six sections. The first section is an introduction. In the second section, we present the method used to estimate the variance of the mortality rate and then estimate the VAR of reserves from these variances. In the third section, we explore how to use stochastic interest rate model to estimate the reserve's VAR and the VAR associated with the parameter risk of the interest rate model. In the fourth section, we analyze the contribution of the lapse rate risk and the parameter risk of the lapse rate model to the reserve's VAR. We also analyze the relative significance of the interest rate risk, the lapse rate risk, and the mortality rate risk in terms of their marginal contributions to the VAR of an insurer's reserves in this section. In the fifth section, we calculate the confidence intervals of the VAR estimates discussed in the previous sections. The last section is the conclusion section containing our conclusions and discussions about potential future researches. 涉險值 (風險值) 風險因子死亡率風險解約率風險利率風險保單責任準備金參數風險涉險值的信賴區間 mortality risk interest rate risk lapse rate risk estimation risk (parameter risk) policy reserve risk factor
75	Sur les familles des lois de fonction de hasard unimodale : applications en fiabilité et analyse de survie Saaidia, Noureddine 24 June 2013 (has links) En fiabilité et en analyse de survie, les distributions qui ont une fonction de hasard unimodale ne sont pas nombreuses, qu'on peut citer: Gaussienne inverse ,log-normale, log-logistique, de Birnbaum-Saunders, de Weibull exponentielle et de Weibullgénéralisée. Dans cette thèse, nous développons les tests modifiés du Chi-deux pour ces distributions tout en comparant la distribution Gaussienne inverse avec les autres. Ensuite nousconstruisons le modèle AFT basé sur la distribution Gaussienne inverse et les systèmes redondants basés sur les distributions de fonction de hasard unimodale. / In reliability and survival analysis, distributions that have a unimodalor $\cap-$shape hazard rate function are not too many, they include: the inverse Gaussian,log-normal, log-logistic, Birnbaum-Saunders, exponential Weibull and power generalized Weibulldistributions. In this thesis, we develop the modified Chi-squared tests for these distributions,and we give a comparative study between the inverse Gaussian distribution and the otherdistributions, then we realize simulations. We also construct the AFT model based on the inverseGaussian distribution and redundant systems based on distributions having a unimodal hazard ratefunction. Distribution Gaussienne inverse, Distribution log-normale, Distribution log-logistique, Distribution de Birnbaum-Saunders, Distribution de Weibull exponentielle, Distribution de Weibull généralisée, Test du Chi-deux, Test modifié du Chi-deux, Fiabilité, Analyse de survie, Modèle de Sedyakin, Modèle AFT, Systèmes redondants, Intervalle de confiance, Temps de panne, Maximum de vraisemblance, Estimation, Classes de Neyman-Pearson. Inverse Gaussian distribution, Log-normal distribution, Log-logistic distribution, Birnbaum-Saunders Distribution , Exponential Weibull distribution, Power generalized Weibull distribution, Chi-square test, Modified Chi-squared, Reliability, Survival analysis, Sedyakin's model, AFT model, Redundant system, Confidence interval, Failure time, Maximum likelihood , Estimation, Neyman-Pearson classes Maximum de vraisemblance,
76	Statistical Inference Chou, Pei-Hsin 26 June 2008 (has links) In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications. finite population correction factor statistical hypothesis type I error composite hypothesis power Central limit theorem Basu theorem critical value goodness of fit test likelihood ratio test Lehmann-Scheffe theorem complete statistic ancillary statistic P-value type II error Rao-Blackwell theorem simple hypothesis one-sided test two-sided test significance level sufficient statistic alternative hypothesis testing hypothesis null hypothesis rejection region confidence interval confidence level minimum variance unbiased estimator interval estimation uniformly most powerful test Cramer-Rao inequality likelihood function mean square error moment estimator error of estimation point estimation maximum likelihood estimator bias consistent estimator minimal sufficient statistic factorization theorem unbiased estimator statistic most powerful test test statistics Neyman-Pearson lemma decision rule

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