ROBUSTNESS OF STATISTICAL METHODS AND NONPARAMETRIC STATISTICS

Transcription

1 ROBUSTNESS OF STATISTICAL METHODS AND NONPARAMETRIC STATISTICS

2 THEORY AND DECISION LIBRARY General Editors: W. Leinfellner and G. Eberlein Series A: Philosophy and Methodology of the Social Sd Editors: W. Leinfellner (University of Nebraska) G. Eberlein (University of Technology, Munich: Series B: Mathematical and Statistical Methods Editor: H. Skala (University of Paderborn) Series C: Game Theory and Decision Making Editor: S. Tijs (University of Nijmegen) Series D: Organization and Systems Theory Editor: W. Janko (University of Karlsruhe) SERIES B: MATHEMATICAL AND STATISTICAL METHODS Editor: H. Skala (Paderborn) Editorial board J. Aczel (Walerloo), G. Bamberg (Augsburg), W. Eichhorn (Karlsruhe), P. Fishburn (New Jersey), D. Fraser (Toronto), B. Fuchssteiner (Paderborn) W. Janko (Karlsruhe), P. de Jong (Vancouver), M. Machina (San Diego), A. Rapoport (Toronto), M. Richter (Aachen), D. Sprott (Waterloo), P. Suppes (Stanford), H. Theil (Florida), E. Trillas (Madrid), L. Zadeh (Berke Scope The series focuses on the application of methods and ideas of logic, m: and statistics to the social sciences. In particular, formal treatment phenomena, the analysis of decision making, information theory and pi infe:rence will be central themes of this part of the library. Besides results, empirical investigations and the testing of theoretical models of problems will be subjects of interest. In addition to emphasizing interd communication, the series will seek to support the rapid dissemination results.

3 ROBUSTNESS OF STATISTICAL METHODS AND NONPARAMETRIC STATISTICS Edited by Dieter Rasch and Moti La! Tiku D. REIDEL PUBLISHING COMPANY A MEMBER OF THE KLUWER ACADEMIC PUBLISHERS GROUP [)OR[)RECHT / ROSTON / LANCASTER / TOKYO

4 Library of Congress Cataioging-in-Publication Data Main entry under title: Robustness of statistical methods and nonparametric statistics. 1. Robust statistics - Addresses, essays, lectures. 2. Nonparametric statistics - Addresses, essays, lectures. I. Rasch, Dieter. II. Tiku, Moti Lal. QA R ISBN-13: e-isbn-13: : / Distributors for the Socialist countries VEB Deutscher Verlag der Wissenschaften, Berlin Distributors for the U.S.A. and Canada Kluwer Academic Publishers, 190 Old Derby Street, Hingham, MA 02043, U.S.A. Distributors for all remaining countries Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, Holland. Published by VEB Deutscher Verlag der Wissenschaften, Berlin in co-edition with D. Reidel Publishing Company, Dordrecht, Holland. All Rights 1984 by iaoademy of Agricultural Sciences of the GDR, Research Centre of Animal Production, Dummerstorf-Rostock, DDR 2551 Dummerstorf. Softcover reprint of the hardcover 1st edition 1984 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

5 Preface This volume contains most of the invited and contributed papers presented at the Conference on Robustness of Statistical Methods and Nonparametric Statistics held in the castle oj'schwerin, Mai 29 - June This conference was organized by the Mathematical Society of the GDR in cooperation with the Society of Physical and Mathematical Biology of the GDR, the GDR-Region of the International Biometric Society and the Academy of Agricultural Sciences of the GDR. All papers included were thoroughly reviewed by scientist listed under the heading "Editorial Collaboratories '. Some contributions, we are sorry to report, were not recommended for publication by the rf'vif'wers and do not appear in these proceedings. The editors thank the reviewers for their valuable comments and suggestions. The conference was organizf'd bv a Programme Committee, its chairman was Prof. Dr. Dieter Rasch (Research Centre of Animal Production, Dummerstorf-Rostock). The members of the Programme Committee were Prof. Dr.,Johannes Adam (Martin-Luther-University Halle) Prof. Dr. Heinz Ahrens (Academy of Sciences of the GDR, Berlin) Doz. Dr. Jana Jureckova (Charles University Praha) Prof. Dr. Moti Lal Tiku (McMaster University, Hamilton, Ontario) The aim of the conference was to discuss several aspects of robustness but mainly to present new results regarding the robustness of classical statistical methods especially tests, confidence estimations, and selection procedures, and to compare their performance with nonparametric procedures. Robustness in this sens~ is understood as intensivity against. violation of the normal assumption. Three approaches can be found analytical approach for continuous distributions combinatorial approach for k-point distributions simulations in a system of distributions (Pearson system, Fleishmann system) The simulation studies were well designed and some papers deal with testing the pseudo-random number generators used. Most of the results have not been published elsewhere and appear in these proceedings for the first time. Some papers deal with the robustness issues on the lines of Huber although the main emphasis of the conference was to study robustness in the Pearson framework. Some papers deal with robust experimental designs and some with nonparametric methods (classification, estimation, etc.). We thank the members of the programme committee, the assistant editor, the reviewers and the contributors of papers for their cooperation and assistance in making these proceedings possible. Dieter Rasch and Moti Lal Tiku Rostock and Hamilton February 1984

6 ROBUSTNESS OF STATISTICAL METHODS AND NON PARAMETRIC STATISTICS Edited by Dieter Rasch and Mali LaJ Tiku Proceedings of a Conference held on these topics at Schwerin May 29 - June Organized by the Mathematical Society of the GDR Editors: Dieter Rasch Research Centre of Animal Production Dummerstorf-Rostock of the Academy of Agricultural Sciences of the GDR and Mathematical Department of Wilhelm Pieck University Rostock, GDR Moti Lal Tiku Department of Statistics McMaster University, Hamilton (Ontario), Canada Assistent Editor: Gunter Herrendorfer Research Centre of Animal Production Dummerstorf-Rostock of the Academy of Agricultural Sciences of the GDR Editorial Collaboratories: Ahrens, H. (Berlin); Atkinson, A. (London); Bellach, J. (Berlin); Bunke, H. (Berlin); Dijkstra, J. B. (Eindhoven); Enderlein, G. (Berlin); Enke, H. (Halle); Field, Ch. (Halifax); Gaffke, N. (Aachen); Heckendorff, H. (Karl-Marx-Stadt); Herrendorfer, G. (Rostock); Hischer, K. (Rostock); Horn, M. (Jena); Jureckova,.T. (Prag); Laan, P. van der (Wageningen); Liese, F. (Jena); Neumann, P. (Dresden); Pilz, J. (Freiberg); Posten, H. O. (Connecticut); Rasch, D. (Rostock); Rudolph, E. (Rostock) ; Schmidt, W. (Berlin); Tiku, M. L. (Hamilton); Toutenburg, H. (Berlin); Verdooren, P. (Wageningen); Zielinski, R. (Warschau); Zwanzig, S. (Berlin)

7 CONTENTS Page ANTOCH, J.: Behaviour of L-estimators of location from the point of view of large deviations 5-8 ATKINSON, A. C.: Simulation in research on linear models 9-12 BEDNARSKI, T.: Note about solutions of asymptotic minimax test problems for special capacities BOCK, J.: Some remarks on the comparison of means in the case of correlatej errors DIJKSTRA, J. B.: Robustness of multiple comparisons against variance heterogeneity DOMANSKI, C.: The power of run test verifying the hypothesis of model linearity DOMRbSE, H.: The robustness of selection procedures investigated by a combinatiorial method FEIGE, K.-D.; GUIARD, V.; HERRENDbRFER, G.; HOFFMANN, J.; NEU- MANN, P.; PETERS, H.; RASCH, D.; VETTERMANN, TH.: Results of comparisons between different random number generators FRICK, D.: Robustness of the two-sample sequential t-test GAFFKE, N.: Optimal designs for contaminated linear regression GUIARD, V.: Systems of one-dimensional continuous distributions and their application in simulation studies HERRENDbRFER G.; FEIGE, K.-D.: A combinatorial method in robustness research and two applications HORN, M.: Analogy of the linear regression and the two-sample problem in robustness investigations JURECKOVA, J.: Rates of consistency of classical one-sided tests KHARIN, Y. S.: Asymptotic robustness of Bayesian decision rules in statistical decision theory LAAN, P. van del'; JOS DE KROON: Ranks, standardized ranks and standardized aligned ranks in the analysis of Friedman's block design LIESE, F.: ChernolI type bounds of errors in hypothesis testing of diffusion processes MONTFORT, M. A. J. van; L. R. VERDOOREN: Power simulation with the same random sequences under the null hypothesis and the alternative NORNBERG, G.: Robustness of two-sample tests for variances NORNBERG, G.; RASCH, D.: The influence of different shapes of distributions with the same first foul' moments on robustness PILZ, J.:. Robust Bayes regression estimation under weak prior knowledge PINCUS, R: Distribution of the maximal GAP in a sample and its application for outlier detection POSTEN, H. 0.: Robustness of the two-sample t-test RASCH, D.: Robustness of three sequential one-sample tests against non-normality HASCH, D.; SCHIMKE, E.: A test for exponential regression and its robustness RIEDEL, M.: Comparison of break points of estimators * 3

8 RIZZI, A.: The robustness of some statistical tests. The Multivariate case ROEDEL, E.: Tests for independence in the family of continuous bivariate distributions with finite contingency RUDOLPH, E.: Robustness of many-one statistics 128-1:33 SCHMIDT, W. H.; S. ZWANZIG: Testing hypotheses in nonlinear regression for nonnormal distributions STANIEWSKI, P.: The bootstrap in nonlinear regression STROBY, R: Sharp inequalities for error probabilities of tests under moment conditions TEUSCHER, F.: Simulation studies on robustness of the t- and u-test against truncation of the normal distribution TIKU, M. L.: Robust location-tests and classification procedures TOUTENBURG, H.: Minimax-linear estimation under incorrect prior information TUCHSCHERERA.: The roubstness of some procedures for the two-sample location problem - a simulation study (concept) W ASILEWSK I, Z.: On the measurement of the tests robustness ZIELINSKI, R; ZIELINSKI, W.: A Robust Estimate of Variance in a Linear Model ZIELINSKI, R: Minimax-versus robust experimental designs: Two simple examples WIl 4