
Partial Least Squares Regression
and Related Dimension Reduction Methods
- 456 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Partial Least Squares Regression
and Related Dimension Reduction Methods
About this book
Partial least squares (PLS) regression is, at its historical core, a black-box algorithmic method for dimension reduction and prediction based on an underlying linear relationship between a possibly vector-valued response and a number of predictors.
Through envelopes, much more has been learned about PLS regression, resulting in a mass of information that allows an envelope bridge that takes PLS regression from a black-box algorithm to a core statistical paradigm based on objective function optimization and, more generally, connects the applied sciences and statistics in the context of PLS. This book focuses on developing this bridge. It also covers uses of PLS outside of linear regression, including discriminant analysis, non-linear regression, generalized linear models and dimension reduction generally.
Key Features:
• Showcases the first serviceable method for studying high-dimensional regressions.
• Provides necessary background on PLS and its origin.
• R and Python programs are available for nearly all methods discussed in the book.
This book can be used as a reference and as a course supplement at the Master's level in Statistics and beyond. It will be of interest to both statisticians and applied scientists.
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Information
Table of contents
- Cover Page
- Half-Title Page
- Title Page
- Copyright Page
- Dedication Page
- Contents
- Preface
- Notation and Definitions
- Authors
- List of Figures
- List of Tables
- 1 Introduction
- 2 Envelopes for Regression
- 3 PLS Algorithms for Predictor Reduction
- 4 Asymptotic Properties of PLS
- 5 Simultaneous Reduction
- 6 Partial PLS and Partial Envelopes
- 7 Linear Discriminant Analysis
- 8 Quadratic Discriminant Analysis
- 9 Non-linear PLS
- 10 The Role of PLS in Social Science Path Analyses
- 11 Ancillary Topics
- A Proofs of Selected Results
- Bibliography
- Index