A First Course in Linear Models and Design of Experiments

ISBN-13: 9789811586583 / Angielski / Twarda / 2020 / 230 str.

N. R. Mohan Madhyastha; S. Ravi; A. S. Praveena

Spis treści

Linear Estimation.- Linear Hypotheses and Their Tests.- Block Designs.- Row-Column Designs.- Factorial Experiments.- Analysis of Covariance.- Missing Plot Technique.- Split Plot Design.

O autorze

N. R. Mohan Madhyastha is a former professor of Statistics at the Department of Studies in Statistics, University of Mysore, India. His areas of interest include probability theory, distribution theory, probability theory on metric spaces, stochastic processes, linear models, and design and analysis of experiments. His research articles have been published in several journals of repute. He earned his Ph.D. and M. Sc. in Statistics from the University of Mysore, where he later served for more than 30 years.

S. Ravi is Professor of Statistics at the Department of Studies in Statistics, University of Mysore, India. Earlier, he served as Lecturer in Statistics at the Department of Statistics, University of Mumbai, India, during 1994–97. He earned his Ph.D. in Statistics in 1992 under the supervision of Prof. N. R. Mohan Madhyastha with the thesis titled "Contributions to Extreme Value Theory". With over 35 research articles published in several journals of repute, Prof. Ravi has supervised 8 students to receive their Ph.D. degrees. His areas of research include probability theory, distribution theory, stochastic processes, reliability theory, linear models, regression analysis, design and analysis of experiments, demography, and computational statistics.

A. S. Praveena is Assistant Professor (under the UGC-Faculty Recharge Program) at the Department of Studies in Statistics, University of Mysore, India. She completed her Ph.D. in Statistics from the University of Mysore under the supervision of Prof. S. Ravi. Her research articles have been published in peer reviewed journals of repute. She has 13 years of experience teaching undergraduate and postgraduate students and has presented several R demonstrations in workshops and faculty development programs. She received an award for best poster presentation at the 103rd Indian Science Congress held in the year 2016.

Blurb

This textbook presents the basic concepts of linear models, design and analysis of experiments. With the rigorous treatment of topics and provision of detailed proofs, this book aims at bridging the gap between basic and advanced topics of the subject. Initial chapters of the book explain linear estimation in linear models and testing of linear hypotheses, and the later chapters apply this theory to the analysis of specific models in designing statistical experiments.

The book includes topics on the basic theory of linear models covering estimability, criteria for estimability, Gauss–Markov theorem, confidence interval estimation, linear hypotheses and likelihood ratio tests, the general theory of analysis of general block designs, complete and incomplete block designs, general row column designs with Latin square design and Youden square design as particular cases, symmetric factorial experiments, missing plot technique, analyses of covariance models, split plot and split block designs. Every chapter has examples to illustrate the theoretical results and exercises complementing the topics discussed. R codes are provided at the end of every chapter for at least one illustrative example from the chapter enabling readers to write similar codes for other examples and exercise