Optimal Covariate Designs Theory and Applications
This book primarily addresses the optimality aspects of covariate designs. A covariate model is a combination of ANOVA and regression models. Optimal estimation of the parameters of the model using a suitable choice of designs is of great importance; as s
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l Covariate Designs Theory and Applications
Optimal Covariate Designs
Premadhis Das Ganesh Dutta Nripes Kumar Mandal Bikas Kumar Sinha •
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Optimal Covariate Designs Theory and Applications
123
Premadhis Das Department of Statistics University of Kalyani Kalyani India
Nripes Kumar Mandal Department of Statistics University of Calcutta Kolkata India
Ganesh Dutta Department of Statistics Basanti Devi College (Affiliated to University of Calcutta) Kolkata India
Bikas Kumar Sinha Indian Statistical Institute Kolkata India
ISBN 978-81-322-2460-0 DOI 10.1007/978-81-322-2461-7
ISBN 978-81-322-2461-7
(eBook)
Library of Congress Control Number: 2015942803 Springer New Delhi Heidelberg New York Dordrecht London © Springer India 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer (India) Pvt. Ltd. is part of Springer Science+Business Media (www.springer.com)
The greatest gifts we ever had were the gifts from god we call them parents In memory of My Father Late Jadunandan Das and My Mother Late Sankari Das Premadhis Das Dedicating to My Father Shri Amarendra Prasad Dutta and to My Mother Shrimati Sankari Dutta for their Love, Affection & Blessings Ganesh Dutta In Living Memory of My Parents Late Jatindranath Mandal and Late Bidyutlata Mandal Nripes Kumar Mandal Remembering My Parents Late Birendra Nath Sinha and Late Jogmaya Sinha for their Love, Affection & Blessings Bikas Kumar Sinha
Foreword
It is a standard classroom exercise to assert that in a simple linear regression model involving only one regressor [or, covariate] x, viz., y ¼ α þ βx þ error, the covariate-values (x), assumed to be continuous and to lie in a finite nondegenerate interval a x b, should allow for maximum dispersion in order that the regression parameters can be estimated with the highest efficiency. This suggests a 50–50 split of the total number of observations, i.e., the set of observations are to be generated by setting the covariate (x) at the two extreme
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