WILEY SERIES IN PROBABILITY AND STATISTICS

Transcription

1 I I W I L E Y E n v i r o n m e n t a l S t a t i s t i c s M e t h o d s a n d A p p l i c a t i o n s V i c B a r n e t t WILEY SERIES IN PROBABILITY AND STATISTICS

2 Environmental Statistics

3 WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors: David J. Balding, Peter Bloomfield, Noel A. C. Cressie, Nicholas I. Fisher, Iain M. Johnstone, J. B. Kadane, Geert Molenberghs, Louise M. Ryan, David W. Scott, Adrian F. M. Smith, Jozef L. Teugets Editors Emeriti: Vic Barnett, J. Stuart Hunter, David G. Kendall A complete list of the titles in this series appears at the end of this volume.

4 E n v i r o n m e n t a l S t a t i s t i c s M e t h o d s a n d A p p l i c a t i o n s VIC BARNETT Nottingham Trent University, UK John Wiley & Sons, Ltd

5 Copyright 2004 by John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO!9 8SQ, England Telephone (+44) (for orders and customer service enquiries): Visit our Home Page or Reprinted November 2004, February 2006 All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying. recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London WIT 4LP UK. without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester. West Sussex P019 8SQ, England, or ed to permreq@wiley.co.uk, or faxed to (+44) This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA , USA Wiley-VCH Verlag GmbH, Boschstr. 12, D Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore John Wiley & Sons (Canada) Ltd, 22 Worcester Road, Etobicoke, Ontario M9W 1L1 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Barnett, Vic. Environmental statistics / Vic Barnett. p. cm.-(wiley series in probability and statistics) Includes bibliographical references and index. ISBN 0^171^ (acid-free paper) I, Mathematical statistics. 2. Environmental sciences-statistical methods. I. Title. II. Series. QA276.B dc British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-10: (hbk) ISBN-13: (hbk) Typeset in 10/12pt Times by Kolam Information Services Pvt. Ltd, Pondicherry, India. Printed and bound in Great Britain by Biddies Ltd, King's Lynn. Norfolk This book is printed on acid-free paper responsibly manufactured from sustainable forestry, in which at least two trees are planted for each one used for paper production.

6 T o H a n n a h

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8 C o n t e n t s Preface xiii Chapter 1 Introduction Tomorrow is too Late! Environmental Statistics Some Examples 'Getting it all together' Tn time and space' 'Keep it simple' 'How much can we take?' 'Over the top' Fundamentals Bibliography 18 PART I EXTREMAL STRESSES: EXTREMES, OUTLIERS, ROBUSTNESS 21 Chapter 2 Ordering and Extremes: Applications, models, inference Ordering the Sample Order statistics Order-based Inference Extremes and Extremal Processes Practical study and empirical models; generalized extreme-value distributions Peaks over Thresholds and the Generalized Pareto Distribution 40 Chapter 3 Outliers and Robustness What is an Outlier? Outlier Aims and Objectives Outlier-Generating Models Discordancy and models for outlier generation Tests of discordancy for specific distributions Multiple Outliers: Masking and Swamping 53

9 VIII CONTENTS 3.5 Accommodation: Outlier-Robust Methods A Possible New Approach to Outliers Multivariate Outliers ^6 3.8 Detecting Multivariate Outliers Principles Informal methods Tests of Discordancy Accommodation Outliers in linear models Robustness in General 72 PART II COLLECTING ENVIRONMENTAL DATA: SAMPLING AND MONITORING 75 Chapter 4 Finite-Population Sampling A Probabilistic Sampling Scheme Simple Random Sampling Estimating the mean, X Estimating the variance, S Choice of sample size, n Estimating the population total, A> Estimating a proportion, P Ratios and Ratio Estimators The estimation of a ratio Ratio estimator of a population total or mean Stratified (simple) Random Sampling Comparing the simple random sample mean and the stratified sample mean Choice of sample sizes Comparison of proportional allocation and optimum allocation Optimum allocation for estimating proportions Developments of Survey Sampling 103 Chapter 5 Inaccessible and Sensitive Data Encountered Data Length-Biased or Size-Biased Sampling and Weighted Distributions Weighted distribution methods Composite Sampling Attribute Sampling Continuous variables Estimating mean and variance 115

10 CONTENTS ix 5.4 Ranked-Set Sampling The ranked-set sample mean Optimal estimation Ranked-set sampling for normal and exponential distributions Imperfect ordering 126 Chapter 6 Sampling in the Wild Quadrat Sampling Recapture Sampling The Petersen and Chapman estimators Capture-recapture methods in open populations Transect Sampling The simplest case: strip transects Using a detectability function Estimating/(y) Modifications of approach Point transects or variable circular plots Adaptive Sampling Simple models for adaptive sampling 149 PART III EXAMINING ENVIRONMENTAL EFFECTS: STIMULUS-RESPONSE RELATIONSHIPS 151 Chapter 7 Relationship: regression-type models and methods Linear Models The linear model The extended linear model The normal linear model Transformations Looking at the data Simple transformations General transformations The Generalized Linear Model 171 Chapter 8 Special Relationship Models, Including Quantal Response and Repeated Measures Toxicology Concerns Quantal Response Bioassay Repeated Measures 182