Empirical Likelihood Ratio Tests with Smoothing Estimators and a Weighted Approach for Two Sample Comparison Under Current Status Data PDF Download
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Author: 許玳瑜
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: 許玳瑜
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: 侯科宇
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Paul Shen
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 19
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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.
Author:
Publisher: Morgan Kaufmann
ISBN: 0080963544
Category : Mathematics
Languages : en
Pages : 667
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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
Author: Christian Tönsing
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Abstract: Likelihood ratios are frequently utilized as basis for statistical tests, for model selection criteria and for assessing parameter and prediction uncertainties, e.g. using the profile likelihood. However, translating these likelihood ratios into p-values or confidence intervals requires the exact form of the test statistic's distribution. The lack of knowledge about this distribution for nonlinear ordinary differential equation (ODE) models requires an approximation which assumes the so-called asymptotic setting, i.e. a sufficiently large amount of data. Since the amount of data from quantitative molecular biology is typically limited in applications, this finite-sample case regularly occurs for mechanistic models of dynamical systems, e.g. biochemical reaction networks or infectious disease models. Thus, it is unclear whether the standard approach of using statistical thresholds derived for the asymptotic large-sample setting in realistic applications results in valid conclusions. In this study, empirical likelihood ratios for parameters from 19 published nonlinear ODE benchmark models are investigated using a resampling approach for the original data designs. Their distributions are compared to the asymptotic approximation and statistical thresholds are checked for conservativeness. It turns out, that corrections of the likelihood ratios in such finite-sample applications are required in order to avoid anti-conservative results
Author: Albert Vexler
Publisher: CRC Press
ISBN: 1315353016
Category : Mathematics
Languages : en
Pages : 622
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Statistical Testing Strategies in the Health Sciences provides a compendium of statistical approaches for decision making, ranging from graphical methods and classical procedures through computationally intensive bootstrap strategies to advanced empirical likelihood techniques. It bridges the gap between theoretical statistical methods and practical procedures applied to the planning and analysis of health-related experiments. The book is organized primarily based on the type of questions to be answered by inference procedures or according to the general type of mathematical derivation. It establishes the theoretical framework for each method, with a substantial amount of chapter notes included for additional reference. It then focuses on the practical application for each concept, providing real-world examples that can be easily implemented using corresponding statistical software code in R and SAS. The book also explains the basic elements and methods for constructing correct and powerful statistical decision-making processes to be adapted for complex statistical applications. With techniques spanning robust statistical methods to more computationally intensive approaches, this book shows how to apply correct and efficient testing mechanisms to various problems encountered in medical and epidemiological studies, including clinical trials. Theoretical statisticians, medical researchers, and other practitioners in epidemiology and clinical research will appreciate the book’s novel theoretical and applied results. The book is also suitable for graduate students in biostatistics, epidemiology, health-related sciences, and areas pertaining to formal decision-making mechanisms.
Author: 李均鵬
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Richard L. Dykstra
Publisher:
ISBN:
Category : Nonparametric statistics
Languages : en
Pages : 28
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The likelihood ratio principle is employed to suggest a nonparametric test for testing equality of two distributions against a stochastic ordering alternative. The test appears to be robust against a wide range of alternatives. Percentage points for sample sizes less than or equal to twenty are provided as well as a comparison of power values for the Kolmogorov-Smirnov and Mann-Whitney-Wilcoxon tests. (Author).
Author: Kim P. Huynh
Publisher: Emerald Group Publishing
ISBN: 1787567257
Category : Business & Economics
Languages : en
Pages : 344
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This volume of Advances in Econometrics contains a selection of papers presented at the 'Econometrics of Complex Survey Data: Theory and Applications' conference organized by the Bank of Canada, Ottawa, Canada, from October 19-20, 2017.
Author: Shana Leigh Carter
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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