Overview
- Is a unique book for studies of kernel distribution estimators and their application to statistical inference
- Provides basic tools to help enable the study of nonparametric inference
- Uses many of the results presented here to facilitate machine learning
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
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Table of contents (5 chapters)
Keywords
About this book
This book presents a study of statistical inferences based on the kernel-type estimators of distribution functions. The inferences involve matters such as quantile estimation, nonparametric tests, and mean residual life expectation, to name just some. Convergence rates for the kernel estimators of density functions are slower than ordinary parametric estimators, which have root-n consistency. If the appropriate kernel function is used, the kernel estimators of the distribution functions recover the root-n consistency, and the inferences based on kernel distribution estimators have root-n consistency. Further, the kernel-type estimator produces smooth estimation results. The estimators based on the empirical distribution function have discrete distribution, and the normal approximation cannot be improved—that is, the validity of the Edgeworth expansion cannot be proved. If the support of the population density function is bounded, there is a boundary problem, namely the estimator does not have consistency near the boundary. The book also contains a study of the mean squared errors of the estimators and the Edgeworth expansion for quantile estimators.
Authors and Affiliations
About the authors
Rizky Reza Fauzi: His major field is mathematical statistics, and he got Ph.D. in 2020. He has good skill of mathematics and published 4 papers. He will be one of the leading researchers in Indonesia.
Yoshihiko Maesono: He published about 50 papers which study nonparametric inference. In the last 20 years, he has been studying kernel-type estimation and obtained new theoretical results, especially the methods based on kernel estimation of the distribution function.
Bibliographic Information
Book Title: Statistical Inference Based on Kernel Distribution Function Estimators
Authors: Rizky Reza Fauzi, Yoshihiko Maesono
Series Title: SpringerBriefs in Statistics
DOI: https://doi.org/10.1007/978-981-99-1862-1
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
Softcover ISBN: 978-981-99-1861-4Published: 01 June 2023
eBook ISBN: 978-981-99-1862-1Published: 31 May 2023
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: VIII, 96
Number of Illustrations: 14 b/w illustrations, 1 illustrations in colour
Topics: Statistical Theory and Methods, Applied Statistics, Probability Theory and Stochastic Processes, Applications of Mathematics