Empirical Likelihood Methods For Dependent Functional Data
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Empirical Process Techniques for Dependent Data
Author: Herold Dehling
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,
Empirical Likelihood Methods for Dependent Functional Data
In this dissertation, we develop likelihood based inferences for dependent functional data analysis. This is done by utilizing the empirical likelihood framework, which provides likelihood based inferences without stringent parametric model assumptions. We first consider an adjusted block-wise empirical likelihood (ABEL) method that is designed to work with weakly dependent multivariate data. This method removes the upper limit on the coverage probability of the empirical likelihood confidence region, and the adjustment tuning parameter in ABEL is shown to be related to the Bartlett correction factor. Indeed, by selecting the tuning parameter accordingly, we can achieve the Bartlett corrected coverage error rate. In the setting of a functional AR(1) model, we then propose a maximum empirical likelihood estimator for the kernel operator. Furthermore, we discuss a framework for applying the empirical likelihood method to more general models for dependent functional data. Our method combines basis expansions with a penalization approach, and it allows the number of basis functions used in the expansion to grow as sample size increases. This allows us to obtain a maximum empirical likelihood estimator that converges to the fully functional true parameter of interest. Similar to ABEL, our method breaks free from the convex hull constraint; therefore, it provides an empirical likelihood confidence region with improved coverage accuracy. Automatic tuning parameter selection is also discussed.
Empirical Likelihood and Quantile Methods for Time Series
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.