Multivariate Techniques: An Example Based Approach

276 Pages·2019·40.955 MB·English

by  Saman Hanif Shahbaz Muhammad Hanif, Muhammad Qaiser Shahbaz

Multivariate
Techniques

Multivariate
Techniques:
An Example Based Approach
By
Muhammad Qaiser Shahbaz,
Saman Hanif Shahbaz
and Muhammad Hanif
Cambridge
Scholars
Publishing
Multivariate Techniques: An Example Based Approach
By Muhammad Qaiser Shahbaz, Saman HanifShahbaz
and Muhammad Hanif
This book first published 2019
Cambridge Scholars Publishing
Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Copyright© 2019 by Muhammad Qaiser Shahbaz,
Saman Hanif Shahbaz and Muhammad Hanif
All rights for this book reserved. No part ofthis book may be reproduced,
stored in a retrieval system, or transmitted, in any fonn or by any means,
electronic, mechanical, photocopying, recording or otherwise, without
the prior pennission ofthe copyright owner.
ISBN (10): 1-5275-4011-1
ISBN (13): 978-1-5275-4011-8
To My Siste rs
Muhammad Qaiser Shahbaz
To My Sons: Khizar, Yousuf andMussa
Saman HaniJShahbaz
To My Parents
MuhammadHaniJ

CONTENTS
Preface ....................................................................................................... IX
Chapter One ................................................................................................ 1
Introduction
Chapter Two ............................................................................................. 33
The Multivariate Nonnal Distribution
Chapter Three ........................................................................................... 73
The Wishart and Related Distributions
Chapter Four ............................................................................................. 85
Inference about Mean Vectors
ChapterFive ............................................................................................ 119
Inference about Covariance Matrices
Chapter Six ............................................................................................. 137
The Multivariate Analysis of Variance
Chapter Seven ......................................................................................... 169
Multivariate Regression Analysis
Chapter Eight .......................................................................................... 207
Canonical Correlation Analysis
Chapter Nine ........................................................................................... 229
Principal Components and Factor Analysis
References ............................................................................................... 263

PREFACE
Multivariate analysis has tremendous applications in many areas of life
and deals with several random variables simultaneously. The data which
arise in practical life are multivariate in nature and hence require
specialized techniques for decision making. Multivariate analyses are
studied in two contexts, namely the multivariate distributions and
multivariate techniques. Both of these contexts have their own
requirements. The multivariate distributions are mainly studied
theoretically whereas the multivariate techniques are studied using real
data.
In this we have given a detailed insight of multivariate distributions
and multivariate techniques. The opening chapter of the book provides an
introduction to multivariate distribution theory and popular multivariate
measures. This chapter also provides a brief review of matrix algebra. One
of the most popular multivariate distributions, the multivariate nonnal
distribution, has been discussed in detail in chapter 2. Some other popular
multivariate distributions have also been discussed in chapter 3. These
include the Wishart distribution, multivariate Beta distribution and Wilk's
distribution.
Chapter 4 and Chapter 5 contain two popular multivariate inferences,
namely inferences about population mean vectors and population
covariance matrices. The multivariate counterpart of students' t statistics,
r2
the Hotelling's statistic has also been discussed in Chapter 4. The
multivariate extension of popular Analysis of Variance (ANOVA), the
multivariate ANOVA, has been given in Chapter 6. This chapter contains
both one way and two way multivariate ANOVA and also provides
methods to conduct inference about several mean vectors.
Chapter 7 of the book is dedicated to another popular multivariate
technique, the multivariate regression analysis. This chapter provides
methods of estimation and hypotheses testing in case of multivariate
regression analysis. The chapter also covers another popular multivariate
technique, the Seemingly Umelated Regression (SUR) models and
contains methods of estimation and hypothesis testing for such a model.
Chapter 8 and Chapter 9 are dedicated to multivariate techniques
which do not have univariate counterpart. Chapter 8 is reserved for a
detailed discussion of one of these techniques, the Canonical Correlation
Analysis (CCA). Various versions of the technique have been discussed