ANOVA with Dependent Errors (SpringerBriefs in Statistics)

✍ Scribed by Yuichi Goto, Hideaki Nagahata, Masanobu Taniguchi, Anna Clara Monti, Xiaofei Xu

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 100
• Edition: 1st ed. 2023
• Category: Library

✦ Synopsis

This book presents the latest results related to one- and two-way models for time series data. Analysis of variance (ANOVA) is a classical statistical method for IID data proposed by R.A. Fisher to investigate factors and interactions of phenomena. In contrast, the methods developed in this book apply to time series data. Testing theory of the homogeneity of groups is presented under a wide variety of situations including uncorrelated and correlated groups, fixed and random effects, multi- and high-dimension, parametric and nonparametric spectral densities. These methods have applications in several scientific fields. A test for the existence of interactions is also proposed. The book deals with asymptotics when the number of groups is fixed and sample size diverges. This framework distinguishes the approach of the book from panel data and longitudinal analyses, which mostly deal with cases in which the number of groups is large. The usefulness of the theory in this book is illustrated by numerical simulation and real data analysis. This book is suitable for theoretical statisticians and economists as well as psychologists and data analysts.

✦ Table of Contents

Preface
Contents
Acronyms
1 Introduction
1.1 Foundations
1.2 Overview of Chapters
References
2 One-Way Fixed Effect Model
2.1 Tests for Time-Dependent Errors
2.1.1 Three Classical and Famous Test Statistics
2.1.2 Likelihood Ratio Test Based on Whittle Likelihood
References
3 One-Way Fixed Effect Model for High-Dimensional Time Series
3.1 Tests for High-Dimensional Time-Dependent Errors
3.1.1 Asymptotics of Fundamental Statistics for High-Dimensional Time Series
3.1.2 Test Statistics for High-Dimensional Time Series
References
4 One-Way Fixed and Random Effect Models for Correlated Groups
4.1 Test for the Existence of Fixed Effects
4.1.1 Classical Test Statistics
4.1.2 A Test Statistic for Correlated Groups
4.2 Test for the Existence of Random Effects
References
5 Two-Way Random Effect Model for Correlated Cells
5.1 Test for the Existence of Random Effects
5.2 Test for the Existence of Random Interactions
References
6 Optimal Test for One-Way Random Effect Model
6.1 Log-Likelihood Ratio Process for One-Way Random Effect Model
6.2 The Hypothesis That the Variance of Random Effect Equals …
6.3 The Hypothesis That the Variance of Random Effects …
References
7 Numerical Analysis
7.1 One-Way Effect Model with Independent Groups
7.1.1 The Empirical Size
7.1.2 The Power
7.2 One-Way Effect Model with Correlated Groups
7.2.1 Setup
7.2.2 Test Results
7.3 Two-Way Effect Model with Correlated Groups
7.3.1 Test for the Existence Random Effects
7.3.2 Test of Interaction Effects
Reference
8 Empirical Data Analysis
8.1 Average Wind Speed Data
Appendix Index
Index