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Some Results About Empirical Likelihood Method
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Book Synopsis Empirical Likelihood by : Art B. Owen
Download or read book Empirical Likelihood written by Art B. Owen and published by CRC Press. This book was released on 2001-05-18 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al
Book Synopsis Some Results about Empirical Likelihood Method by : Zhong Guan
Download or read book Some Results about Empirical Likelihood Method written by Zhong Guan and published by . This book was released on 2001 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Empirical Likelihood Method in Survival Analysis by : Mai Zhou
Download or read book Empirical Likelihood Method in Survival Analysis written by Mai Zhou and published by CRC Press. This book was released on 2015-06-17 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical Likelihood Method in Survival Analysis explains how to use the empirical likelihood method for right censored survival data. The author uses R for calculating empirical likelihood and includes many worked out examples with the associated R code. The datasets and code are available for download on his website and CRAN. The book focuses on all the standard survival analysis topics treated with empirical likelihood, including hazard functions, cumulative distribution functions, analysis of the Cox model, and computation of empirical likelihood for censored data. It also covers semi-parametric accelerated failure time models, the optimality of confidence regions derived from empirical likelihood or plug-in empirical likelihood ratio tests, and several empirical likelihood confidence band results. While survival analysis is a classic area of statistical study, the empirical likelihood methodology has only recently been developed. Until now, just one book was available on empirical likelihood and most statistical software did not include empirical likelihood procedures. Addressing this shortfall, this book provides the functions to calculate the empirical likelihood ratio in survival analysis as well as functions related to the empirical likelihood analysis of the Cox regression model and other hazard regression models.
Book Synopsis Empirical Likelihood and Quantile Methods for Time Series by : Yan Liu
Download or read book Empirical Likelihood and Quantile Methods for Time Series written by Yan Liu and published by Springer. This book was released on 2018-12-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makes analysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.
Book Synopsis Empirical Likelihood Methods in Nonignorable Covariate-missing Data Problems by : Yanmei Xie
Download or read book Empirical Likelihood Methods in Nonignorable Covariate-missing Data Problems written by Yanmei Xie and published by . This book was released on 2019 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. This dissertation contains three topics in nonignorable covariate-missing data problems, in which we study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. First, by exploitation of a probability model of missingness and a working conditional score model from a semiparametric perspective, we propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. These unbiased estimating equations naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. Based on the proposed estimating equations, we introduce three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. By utilizing the proposed empirical likelihood method on a data set from the US National Health and Nutrition Examination Survey (NHANES), we study the effect of daily alcohol consumption on hypertension. Second, we explore unconstrained and constrained empirical likelihood ratio statistics to construct empirical likelihood confidence regions for the underlying regression parameters without and with constraints. We establish the asymptotic distributions of the proposed empirical likelihood ratio statistics. The proposed empirical likelihood methods have a better finite-sample performance than other existing competitors in terms of coverage probability and interval length. An analysis on the data set from the US NHANES demonstrates that increased alcohol consumption per day is significantly associated with increased systolic blood pressure. In addition, higher body mass index and older age have a significantly higher risk of hypertension. Third, we propose a pseudo empirical likelihood ratio statistic, yet it is demonstrated following an asymptotically chi-squared distribution. Our proposed method allows for confidence interval construction without variance estimation and thus is more computationally feasible. Simulation results suggest that the proposed empirical likelihood confidence interval has a better finite-sample performance than the corresponding Wald-based competitor in terms of coverage probability and interval length. Moreover, the proposed empirical likelihood ratio test is always superior to the Wald method in terms of their power performances in our simulation studies.
Book Synopsis Empirical Likelihood and Extremes by : Yun Gong
Download or read book Empirical Likelihood and Extremes written by Yun Gong and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988, Owen introduced empirical likelihood as a nonparametric method for constructing confidence intervals and regions. Since then, empirical likelihood has been studied extensively in the literature due to its generality and effectiveness. It is well known that empirical likelihood has several attractive advantages comparing to its competitors such as bootstrap: determining the shape of confidence regions automatically using only the data; straightforwardly incorporating side information expressed through constraints; being Bartlett correctable. The main part of this thesis extends the empirical likelihood method to several interesting and important statistical inference situations. This thesis has four components. The first component (Chapter II) proposes a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve in order to overcome the computational difficulty when we have nonlinear constrains in the maximization problem. The second component (Chapter III and IV) proposes smoothed empirical likelihood methods to obtain interval estimation for the conditional Value-at-Risk with the volatility model being an ARCH/GARCH model and a nonparametric regression respectively, which have applications in financial risk management. The third component(Chapter V) derives the empirical likelihood for the intermediate quantiles, which plays an important role in the statistics of extremes. Finally, the fourth component (Chapter VI and VII) presents two additional results: in Chapter VI, we present an interesting result by showing that, when the third moment is infinity, we may prefer the Student's t-statistic to the sample mean standardized by the true standard deviation; in Chapter VII, we present a method for testing a subset of parameters for a given parametric model of stationary processes.
Download or read book In All Likelihood written by Yudi Pawitan and published by OUP Oxford. This book was released on 2013-01-17 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.
Book Synopsis Introduction to Empirical Processes and Semiparametric Inference by : Michael R. Kosorok
Download or read book Introduction to Empirical Processes and Semiparametric Inference written by Michael R. Kosorok and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.
Book Synopsis Some Contributions to the Empirical Likelihood Method by : Min Chen
Download or read book Some Contributions to the Empirical Likelihood Method written by Min Chen and published by . This book was released on 2005 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Innovative Strategies, Statistical Solutions and Simulations for Modern Clinical Trials by : Mark Chang
Download or read book Innovative Strategies, Statistical Solutions and Simulations for Modern Clinical Trials written by Mark Chang and published by CRC Press. This book was released on 2019-03-20 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is truly an outstanding book. [It] brings together all of the latest research in clinical trials methodology and how it can be applied to drug development.... Chang et al provide applications to industry-supported trials. This will allow statisticians in the industry community to take these methods seriously." Jay Herson, Johns Hopkins University The pharmaceutical industry's approach to drug discovery and development has rapidly transformed in the last decade from the more traditional Research and Development (R & D) approach to a more innovative approach in which strategies are employed to compress and optimize the clinical development plan and associated timelines. However, these strategies are generally being considered on an individual trial basis and not as part of a fully integrated overall development program. Such optimization at the trial level is somewhat near-sighted and does not ensure cost, time, or development efficiency of the overall program. This book seeks to address this imbalance by establishing a statistical framework for overall/global clinical development optimization and providing tactics and techniques to support such optimization, including clinical trial simulations. Provides a statistical framework for achieve global optimization in each phase of the drug development process. Describes specific techniques to support optimization including adaptive designs, precision medicine, survival-endpoints, dose finding and multiple testing. Gives practical approaches to handling missing data in clinical trials using SAS. Looks at key controversial issues from both a clinical and statistical perspective. Presents a generous number of case studies from multiple therapeutic areas that help motivate and illustrate the statistical methods introduced in the book. Puts great emphasis on software implementation of the statistical methods with multiple examples of software code (both SAS and R). It is important for statisticians to possess a deep knowledge of the drug development process beyond statistical considerations. For these reasons, this book incorporates both statistical and "clinical/medical" perspectives.
Book Synopsis Sample Surveys: Inference and Analysis by :
Download or read book Sample Surveys: Inference and Analysis written by and published by Morgan Kaufmann. This book was released on 2009-09-02 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Statistics_29B contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications. Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume 1 deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume 2 is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects. Comprehensive account of recent developments in sample survey theory and practice Covers a wide variety of diverse applications Comprehensive bibliography
Book Synopsis Contemporary Multivariate Analysis and Design of Experiments by : Kaitai Fang
Download or read book Contemporary Multivariate Analysis and Design of Experiments written by Kaitai Fang and published by World Scientific. This book was released on 2005 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Index. Subject index -- Author index
Book Synopsis Empirical Likelihood Methods in Biomedicine and Health by : Albert Vexler
Download or read book Empirical Likelihood Methods in Biomedicine and Health written by Albert Vexler and published by CRC Press. This book was released on 2018-09-03 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical Likelihood Methods in Biomedicine and Health provides a compendium of nonparametric likelihood statistical techniques in the perspective of health research applications. It includes detailed descriptions of the theoretical underpinnings of recently developed empirical likelihood-based methods. The emphasis throughout is on the application of the methods to the health sciences, with worked examples using real data. Provides a systematic overview of novel empirical likelihood techniques. Presents a good balance of theory, methods, and applications. Features detailed worked examples to illustrate the application of the methods. Includes R code for implementation. The book material is attractive and easily understandable to scientists who are new to the research area and may attract statisticians interested in learning more about advanced nonparametric topics including various modern empirical likelihood methods. The book can be used by graduate students majoring in biostatistics, or in a related field, particularly for those who are interested in nonparametric methods with direct applications in Biomedicine.
Book Synopsis Adjusted Empirical Likelihood Method for Comparison of Treatment Effects in Linear Model Setting by : Kang, Xi
Download or read book Adjusted Empirical Likelihood Method for Comparison of Treatment Effects in Linear Model Setting written by Kang, Xi and published by . This book was released on 2016 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Empirical Likelihood Methods for Pretest-Posttest Studies by : Min Chen
Download or read book Empirical Likelihood Methods for Pretest-Posttest Studies written by Min Chen and published by . This book was released on 2015 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pretest-posttest trials are an important and popular method to assess treatment effects in many scientific fields. In a pretest-posttest study, subjects are randomized into two groups: treatment and control. Before the randomization, the pretest responses and other baseline covariates are recorded. After the randomization and a period of study time, the posttest responses are recorded. Existing methods for analyzing the treatment effect in pretest-posttest designs include the two-sample t-test using only the posttest responses, the paired t-test using the difference of the posttest and the pretest responses, and the analysis of covariance method which assumes a linear model between the posttest and the pretest responses. These methods are summarized and compared by Yang and Tsiatis (2001) under a general semiparametric model which only assumes that the first and second moments of the baseline and the follow-up response variable exist and are finite. Leon et al. (2003) considered a semiparametric model based on counterfactuals, and applied the theory of missing data and causal inference to develop a class of consistent estimator on the treatment effect and identified the most efficient one in the class. Huang et al. (2008) proposed a semiparametric estimation procedure based on empirical likelihood (EL) which incorporates the pretest responses as well as baseline covariates to improve the efficiency. The EL approach proposed by Huang et al. (2008) (the HQF method), however, dealt with the mean responses of the control group and the treatment group separately, and the confidence intervals were constructed through a bootstrap procedure on the conventional normalized Z-statistic. In this thesis, we first explore alternative EL formulations that directly involve the parameter of interest, i.e., the difference of the mean responses between the treatment group and the control group, using an approach similar to Wu and Yan (2012). Pretest responses and other baseline covariates are incorporated to impute the potential posttest responses. We consider the regression imputation as well as the non-parametric kernel imputation. We develop asymptotic distributions of the empirical likelihood ratio statistic that are shown to be scaled chi-squares. The results are used to construct confidence intervals and to conduct statistical hypothesis tests. We also derive the explicit asymptotic variance formula of the HQF estimator, and compare it to the asymptotic variance of the estimator based on our proposed method under several scenarios. We find that the estimator based on our proposed method is more efficient than the HQF estimator under a linear model without an intercept that links the posttest responses and the pretest responses. When there is an intercept, our proposed model is as efficient as the HQF method. When there is misspecification of the working models, our proposed method based on kernel imputation is most efficient. While the treatment effect is of primary interest for the analysis of pretest-posttest sample data, testing the difference of the two distribution functions for the treatment and the control groups is also an important problem. For two independent samples, the nonparametric Mann-Whitney test has been a standard tool for testing the difference of two distribution functions. Owen (2001) presented an EL formulation of the Mann-Whitney test but the computational procedures are heavy due to the use of a U-statistic in the constraints. We develop empirical likelihood based methods for the Mann-Whitney test to incorporate the two unique features of pretest-posttest studies: (i) the availability of baseline information for both groups; and (ii) the missing by design structure of the data. Our proposed methods combine the standard Mann-Whitney test with the empirical likelihood method of Huang, Qin and Follmann (2008), the imputation-based empirical likelihood method of Chen, Wu and Thompson (2014a), and the jackknife empirical likelihood (JEL) method of Jing, Yuan and Zhou (2009). The JEL method provides a major relief on computational burdens with the constrained maximization problems. We also develop bootstrap calibration methods for the proposed EL-based Mann-Whitney test when the corresponding EL ratio statistic does not have a standard asymptotic chi-square distribution. We conduct simulation studies to compare the finite sample performances of the proposed methods. Our results show that the Mann-Whitney test based on the Huang, Qin and Follmann estimators and the test based on the two-sample JEL method perform very well. In addition, incorporating the baseline information for the test makes the test more powerful. Finally, we consider the EL method for the pretest-posttest studies when the design and data collection involve complex surveys. We consider both stratification and inverse probability weighting via propensity scores to balance the distributions of the baseline covariates between two treatment groups. We use a pseudo empirical likelihood approach to make inference of the treatment effect. The proposed methods are illustrated through an application using data from the International Tobacco Control (ITC) Policy Evaluation Project Four Country (4C) Survey.
Book Synopsis EMPIRICAL LIKELIHOOD TESTS FOR CONSTANT VARIANCE IN THE TWO-SAMPLE PROBLEM by : Paul Shen
Download or read book EMPIRICAL LIKELIHOOD TESTS FOR CONSTANT VARIANCE IN THE TWO-SAMPLE PROBLEM written by Paul Shen and published by . This book was released on 2019 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we investigate the problem of testing constant variance. It is an important problem in the field of statistical influence where many methods require the assumption of constant variance. The question of constant variance has to be settled in order to perform a significance test through a Student t-Test or an F-test. Two of most popular tests of constant variance in applications are the classic F-test and the Modified Levene's Test. The former is a ratio of two sample variances. Its performance is found to be very sensitive with the normality assumption. The latter Modified Levene's Test can be viewed as a result of the estimation method through the absolute deviation from the median. Its performance is also dependent upon the distribution shapes to some extent, though not as much as the F-test. We propose an innovative test constructed by the empirical likelihood method through the moment estimation equations appearing in the Modified Levene's Test. The new empirical likelihood ratio test is a nonparametric test and retains the principle of maximum likelihood. As a result, it can be an appropriate alternative to the two traditional tests in applications when underlying populations are skewed. To be specific, the empirical likelihood ratio test of constant variance uses the optimal weights in summing the absolute deviations of observations from the median values, while the Modified Levene's test uses the simple averages. It is thus desired that the empirical likelihood ratio test is more powerful than the Modified Levene's test. Meanwhile, the empirical likelihood ratio test is expected to be as robust as the Modified Levene's test, as the empirical likelihood ratio test is also constructed via the same distance as the Modified Levene's test. A real-life data set is used to illustrate implementation of the empirical likelihood ratio test with comparisons to the classic F-test and the Modified Levene's Test. It is confirmed that the empirical likelihood ratio test performs the best.
Book Synopsis The Two-sample Empirical Likelihood Method by : Bing-Yi Jing
Download or read book The Two-sample Empirical Likelihood Method written by Bing-Yi Jing and published by . This book was released on 1993 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
