Browsing by Author "Emura, Takeshi"

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A goodness-of-fit test for Archimedean copula models in the presence of right censoring
(2010-12-01)
Emura, Takeshi
;
Lin, Chien-Wei
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Wang, Weijing
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統計學研究所
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Institute of Statistics
A goodness-of-fit testing procedure for Archimedean copula (AC) models is developed based on right-censored data. The proposed approach extends an existing method, which is suitable for the Clayton model, to general AC models. Asymptotic properties of the proposed test statistics under the true model assumption are derived. Simulation analysis shows that the proposed test has reasonable performance. Finally, two real data examples are analyzed for illustrative purposes. (C) 2010 Elsevier B.V. All rights reserved.
Approximate Tolerance Limits Under Log-Location-Scale Regression Models in the Presence of Censoring
(2010-08-01)
Emura, Takeshi
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Wang, Hsiuying
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統計學研究所
;
Institute of Statistics
For a product manufactured in large quantities, tolerance limits play a fundamental role in setting limits on the process capability. Existing methodologies for setting tolerance limits in life test experiments focus primarily on one-sample problems. In this study, we extend tolerance limits in the presence of covariates in life test experiments. A method constructing approximate tolerance limits is proposed under log-location-scale regression models, a class of models used widely in reliability and life test experiments. The method is based on an application of the large sample theory of maximum likelihood estimators, which is modified by a bias-adjustment technique to enhance small sample accuracy. The proposed approximate tolerance limits are shown asymptotically to have nominal coverage probability under the assumption of "independent censoring." This includes Type I and Type II censoring schemes. Simulation studies are conducted to assess finite sample properties under the log-location-scale regression models. The method is illustrated with two datasets. R codes for implementing the proposed method are available online on the Technometrics web site, as supplemental materials.
Comments on: Inference in multivariate Archimedean copula models
(2011-08-01)
Wang, Weijing
;
Emura, Takeshi
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統計學研究所
;
Institute of Statistics
Multivariate normal distribution approaches for dependently truncated data
(2012-02-01)
Emura, Takeshi
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Konno, Yoshihiko
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統計學研究所
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Institute of Statistics
Many statistical methods for truncated data rely on the independence assumption regarding the truncation variable. In many application studies, however, the dependence between a variable X of interest and its truncation variable L plays a fundamental role in modeling data structure. For truncated data, typical interest is in estimating the marginal distributions of (L, X) and often in examining the degree of the dependence between X and L. To relax the independence assumption, we present a method of fitting a parametric model on (L, X), which can easily incorporate the dependence structure on the truncation mechanisms. Focusing on a specific example for the bivariate normal distribution, the score equations and Fisher information matrix are provided. A robust procedure based on the bivariate t-distribution is also considered. Simulations are performed to examine finite-sample performances of the proposed method. Extension of the proposed method to doubly truncated data is briefly discussed.
Nonparametric maximum likelihood estimation for dependent truncation data based on copulas
(2012-09-01)
Emura, Takeshi
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Wang, Weijing
;
統計學研究所
;
Institute of Statistics
Truncation occurs when the variable of interest can be observed only if its value satisfies certain selection criteria. Most existing methods for analyzing such data critically rely on the assumption that the truncation variable is quasi-independent of the variable of interest. In this article, the authors propose a likelihood-based inference approach under the assumption that the dependence structure of the two variables follows a general form of copula model. They develop a model selection method for choosing the best-fitted copula among a broad class of model alternatives, and they derive large-sample properties of the proposed estimators, including the inverse Fisher information matrix. The treatment of ties is also discussed. They apply their methods to the analysis of a transfusion-related AIDS data set and compare the results with existing methods. Simulation results are also provided to evaluate the finite-sample performances of all the competing methods. (C) 2012 Elsevier Inc. All rights reserved.
SEMI-PARAMETRIC INFERENCE FOR COPULA MODELS FOR TRUNCATED DATA
(2011-01-01)
Emura, Takeshi
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Wang, Weijing
;
Hung, Hui-Nien
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統計學研究所
;
Institute of Statistics
We investigate the dependent relationship between two failure time variables that truncate each other. Chaieb, Rivest, and Abdous (2006) proposed a semi-parametric model under the so-called "semi-survival" Archimedean-copula assumption and discussed estimation of the association parameter, the truncation probability, and the marginal functions. Here the same model assumption is adopted but different inference approaches are proposed. For estimating the association parameter, we extend the conditional likelihood approach (Clayton (1978)) and the two-by-two table approach (Wang (2003)) to dependent truncation data. We further show that the three estimators, including that proposed by Chaieb, Rivest, and Abdous (2006), differ in weights. The likelihood approach provides the formula for a good weight. Large sample properties of the proposed methods are established by applying the functional delta method, which can handle estimating functions that are not in the form of U-statistics. Analytic formulae for the asymptotic variance estimators are provided. Two competing methods are compared via simulations, and applied to the transfusion-related AIDS data.
Semiparametric inference for an accelerated failure time model with dependent truncation
(2016-10)
Emura, Takeshi
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Wang, Weijing
;
統計學研究所
;
Institute of Statistics
Truncated data are commonly seen in studies of biomedicine, epidemiology, astronomy and econometrics. Existing regression methods for analyzing left-truncated and right-censored data have been developed under the assumption that the lifetime variable of interest is independent of both truncation and censoring variables. In this article, we propose a semiparametric accelerated failure time model that incorporates both covariates and the truncation variable as regressors. The proposed model utilizes the truncation information in statistical modeling and hence allows for dependent truncation. For estimation, we develop a set of estimating equations constructed from the log-rank and quasi-independence test statistics. We show that the resulting estimators are consistent and asymptotically normal. We also propose an explicit formula for variance estimation based on a kernel method. Finite-sample performances of the estimators are studied by simulations. The proposed methodology is applied to analyze a real data for illustration.
Testing quasi-independence for truncation data
(2010-01-01)
Emura, Takeshi
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Wang, Weijing
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交大名義發表
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National Chiao Tung University
Quasi-independence is a common assumption for analyzing truncated data. To verify this condition, we propose a class of weighted log-rank type statistics that include existing tests proposed by Tsai (1990) and Martin and Betensky (2005) as special cases. To choose an appropriate weight function that may lead to a more power test, we derive a score test when the dependence Structure under the alternative hypothesis is modeled via the odds ratio function proposed by Chaieb, Rivest and Abdous (2006). Asymptotic properties of the proposed tests are established based oil the functional delta method which can handle more general Situations than results based oil rank-statistics or U-statistics. Extension of the proposed methodology under two different censoring settings is also discussed. Simulations are performed to examine finite-sample performances of the proposed method and its competitors. Two datasets are analyzed for illustrative purposes. (C) 2009 Elsevier Inc. All rights reserved.