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Author: Bin Dong
Publisher:
ISBN:
Category :
Languages : en
Pages : 131
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Book Description
Empirical likelihood, which was pioneered by Thomas and Grunkemeier (1975) and Owen (1988), is a powerful nonparametric method of statistical inference that has been widely used in the statistical literature. In this thesis, we investigate the merits of empirical likelihood for various problems arising in ratio estimation.
Author: Bin Dong
Publisher:
ISBN:
Category :
Languages : en
Pages : 131
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Book Description
Empirical likelihood, which was pioneered by Thomas and Grunkemeier (1975) and Owen (1988), is a powerful nonparametric method of statistical inference that has been widely used in the statistical literature. In this thesis, we investigate the merits of empirical likelihood for various problems arising in ratio estimation.
Author: Art B. Owen
Publisher: CRC Press
ISBN: 1420036157
Category : Mathematics
Languages : en
Pages : 322
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Book Description
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
Author: Yan Liu
Publisher: Springer
ISBN: 9811001529
Category : Mathematics
Languages : en
Pages : 144
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Book Description
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.
Author: Mai Zhou
Publisher: CRC Press
ISBN: 1466554932
Category : Mathematics
Languages : en
Pages : 221
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Book Description
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.
Author: Albert Vexler
Publisher: CRC Press
ISBN: 1351001507
Category : Mathematics
Languages : en
Pages : 149
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Book Description
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.
Author: Albert Vexler
Publisher: CRC Press
ISBN: 1351001507
Category : Mathematics
Languages : en
Pages : 149
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Book Description
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.
Author: Paul Shen
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 19
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Book Description
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: Yanmei Xie
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 125
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Book Description
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.
Author: Yinghua Lu
Publisher:
ISBN:
Category : Confidence intervals
Languages : en
Pages : 55
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Book Description
In this thesis, we study two methods for inference of parameters in the accelerated failure time model with right censoring data. One is the Wald-type method, which involves parameter estimation. The other one is empirical likelihood method, which is based on the asymptotic distribution of likelihood ratio. We employ a monotone censored data version of Kendall estimating equation, and construct confidence intervals from both methods. In the simulation studies, we compare the empirical likelihood (EL) and the Wald-type procedure in terms of coverage accuracy and average length of confidence intervals. It is concluded that the empirical likelihood method has a better performance. We also compare the EL for Kendall's rank regression estimator with the EL for other well known estimators and find advantages of the EL for Kendall estimator for small size sample. Finally, a real clinical trial data is used for the purpose of illustration.
Author: 許玳瑜
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
