Название: Rank-Based Methods for Shrinkage and Selection
Автор: A. K. Md. Ehsanes Saleh
Издательство: John Wiley & Sons Limited
Жанр: Математика
isbn: 9781119625421
isbn:
Rank-Based Methods for Shrinkage and Selection
With Application to Machine Learning
A. K. Md. Ehsanes Saleh Carleton University, Ottawa, Canada
Mohammad Arashi Ferdowsi University of Mashhad, Mashhad, Iran
Resve A. Saleh University of British Columbia, Vancouver, Canada
Mina Norouzirad Center for Mathematics and Application of NOVA University Lisbon, Lisbon, Portugal
This edition first published 2022
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Library of Congress Cataloging-in-Publication Data
ISBN 9781119625391
Cover image: [Production Editor to insert]
Cover design by [Production Editor to insert]
Set in 9.5/12.5pt STIXTwoText by Integra Software Services Pvt. Ltd, Pondicherry, India
We dedicate this book to
Shahidara Saleh
Reihaneh Soleimani, Elena Arashi
Lynn Hilchie Saleh
Abbas Ali Norouzirad, Fereshteh Arefian
Contents
1 Cover
8 Foreword
9 Preface
10 1 Introduction to Rank-based Regression1.1 Introduction1.2 Robustness of the Median1.2.1 Mean vs. Median1.2.2 Breakdown Point1.2.3 Order and Rank Statistics1.3 Simple Linear Regression1.3.1 Least Squares Estimator (LSE)1.3.2 Theil’s Estimator1.3.3 Belgium Telephone Data Set1.3.4 Estimation and Standard Error Comparison1.4 Outliers and their Detection1.4.1 Outlier Detection1.5 Motivation for Rank-based Methods1.5.1 Effect of a Single Outlier1.5.2 Using Rank for the Location Model1.5.3 Using Rank for the Slope1.6 The Rank Dispersion Function1.6.1 Ranking and Scoring Details1.6.2 Detailed Procedure for R-estimation1.7 Shrinkage Estimation and Subset Selection1.7.1 Multiple Linear Regression using Rank1.7.2 Penalty Functions1.7.3 Shrinkage Estimation1.7.4 Subset Selection1.7.5 Blended Approaches1.8 Summary1.9 СКАЧАТЬ