Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians: held at Prague, from August 18 to 23, 1974

576 Pages·1977·29.987 MB·English

by  Rashid Ahmad (auth.), J. Kožešnik (eds.)

CZECHOSLOVAK ACADEMY OF SCIENCES
CZECHOSLOVAK ACADEMY OF SCIENCES
Scientific Editor: Academician Jaroslav Kozesnik
Editorial Board: Miloslav Driml, Otto Hans, Ivan M. Havel,
Stanislav Jilovec, Vlasta Kankova, Zdenek Koutsky, Ivan Kramosil,
Josef Ki'epela, Libor Kubat, Petr Mandl, Milan Mares, Jifi Michalek,
Jii'i Nedoma, Albert Perez, Karel Sladky, Otakar Sefi, Milan Ullrich,
Karol Vasek, Karel Winkelbauer
Executive Editor: Libor Kubat
TRANSACTIONS
a/the
SEVENTH
PRAGUE CONFERENCE
an
INFORMATION THEORY,
STATISTICAL DECISION FUNCTIONS,
RANDOM PROCESSES
and of the
1974 EUROPEAN MEETING
OF STATISTICIANS
held at
Prague, from August 18 to 23, 1974
VOLUME A
1977
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Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland, in co-edition
with ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
© ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1977
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
or otherwise, without the prior written permission of the publishers
ISBN 978-94-010-9912-7 ISBN 978-94-010-9910-3 (eBook)
DOI 10.1007/978-94-010-9910-3
CONTENTS
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
Invited Papers
Csiszar I.: Information Measures: a Critical Survey. . . . . . .. . vol.B
Durbin J.: Goodness-of-Fit Tests Based on the Order Statistics . .. . vol.B
Gani J.: A Markov Chain for Type Counts in Vocabulary Subgroups 155
Jacobs K.: Recent Developments in Ergodic Theory. . . . . . . . 283
Lukacs E.: A Stability Theorem for a Characterization of the Wiener Process 375
Mandl P.: Some Results in the Adaptive Control of Linear Systems . . . . 399
Metivier M.: Advances in the Theory of Stochastic Integration and Ap-
plications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
Rajbman N. S.: Dispersion Functions of Random Functions and Some their
Applications. . . . . . . . . . . . .. ........ vol.B
Schmetterer L.: Einige Resultate aus der Theorie der erwartungstreuen
Schatzungen. . . . . . . . . . . . . . . . . . . . . . . . . . . . vol. B
Sidak Z.: Miscellaneous Topics in Markov Chains with a General State Space 531
Ullrich M.: The Use of Boolean Functions for Generation of Stochastic
Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vol. B
Communications
Ahmad R.: An Algebraic Treatment of Markov Processes. . . . . . . .. 13
Aksland M.: On Interconnected Birth and Death Processes with Immigration 23
Andel J.: On the Backward Extrapolation of Non-Stationary Autoregressive
Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
Anderson T. W.: On Maximum Likelihood Estimation of Parameters of
Autoregressive Moving Average Processes . . . . . . . . . . . . .. 37
Bandemer H.: Experimental Design in Decision Models ......... vol.B
Bernardo J. M.: Information Theory and Bayesian Design of Experiments .. vol.B
Besag J.: On Spatial-Temporal Models and Markov Fields . . . . . .. 47
Bouchon B.: Quelques resultats de la theorie des questionnaires realisables. . vol. B
Brauer D.: Zur Auswertung des Elektromyogramms mit spektralanalytischen
Methoden. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57
Broussolle C.: L'utilisation de la theorie des phenomenes d'attente dans
I'analyse des systemes de production agricole. . . . . . . . . . . . .. 63
5
Butkiewicz J., Hys E.: On a Class of Bi- and Multivariate Distributions
Generated by Marginal Weibull Distributions. . . . . . . . . . . .. 73
<;apar U.: Random Fixed Point Theorems and Sequential Decision Making
in Abstract Spaces . . . . . . . . . . . . . . . . . . . . . . . . . vol. B
v.:
Capasso On the General Stochastic Epidemic with Immigration in Large
Populations . . . . . . . . . . . . . . . . . . . . . . .. 83
Clifford P.: On the Age Structure of Cell-Size Dependent Branching
Processes . . . . . . . . . . . . . . . . .. . . . . . . . . . 97
Cochlar J.: Smoothing and Extrapolation of Incomplete Time Series. vol.B
0
Conradsen Ko: Some Aspects of the Analysis of Air Pollution Data. vol.B
0 •
Csibi S.: More on Computationally Constrained Learning Processes. . vol.B
Csorgo M., Koml6s J., Major P., Revesz P., Tusnady G.: On the
Empirical Process when Parameters are Estimated . . . . . . . . vol. B
0 • •
Drygas H.: Admissibility of Certain ANOVA-Estimators in Simple Variance-
Component Models. vol. B
0 • • • • • • • • • 0 • • • • • • • • • • • • •
Dziubdziela Wo: On Convergence Rates in the Limit Laws for Extreme Order
Statistics . vol. B
0 0 • • • • • • • • • • 0 • • • • 0 • • • • • • • • • 0
Ephremides Ao: Information Patterns in Stochastic Point Process Differential
Games 103
0 •• 0 •• 0 0 ••••••• 0 ••••••••• 0 ••• 0
Fahrmeir L., Beeck Ho: Zur Simulation stetiger stochastischer Wirtschafts-
modelle 113
0 0 • 0 • • • • • • • 0 • • • • 0 • • • 0 • • 0 • • 0 • ••
Fichtner K. Ho: Poissonsche zufallige Punktfolgen und ortsabh1ingige Ver-
diinnungen 123
0 • • •• • ••• 0 0 • • • • • • • • • • • •
Fieger W.: Die Anzahl der Kreuzungspunkte einer Funktion mit einem
GauBschen ProzeB . . . . . . . . 135
0 • 0 0 • 0 0 • • • • • • 0 • • •
Fleischmann K.: On the Stability of Spatially Homogeneous Cluster Fields 147
0
Ganssler P.: On the Realization of Stochastic Processes by Probability Distri-
butions in Function Spaces . . . . . 163
0 • • • 0 0 • 0 • • • •
Gasser T.: Tests of Goodness-of-Fit for Stationary Processes 173
0 • 0 0 • 0 0 0
Ghosal A.: Cybernetic Modelling of Queueing & Storage Systems .. 181
0 ••
Giguere M. A., Styan G. P. Ho: Multivariate Normal Estimation with
Missing Data on Several Variates vol.B
0 • 0 0 0 • • 0 • • • 0 0 0 • • 0 • 0
Gittins Jo, Nash P.: Scheduling, Queues and Dynamic Allocation Indices.. 191
rrrOHTH O. Ao: IIepe,Il;aqa caYCCOBCKHX CHCHarrOB no KaHarry c 06paTHoH
CBJl3blO vol. B
0 0 • 0 0 0 0 0 0 • 0 0 • 0 0 0 • • • • 0 • • • 0 • • • • •
Goel Ao L., J oglekar A. Mo: Statistical Modelling of Computer Systems:
a Review . vol. B
0 0 • • 0 0 0 • 0 0 • 0 0 • • • 0 • • 0 • • 0 • • • • •
Govindarajulu Zo: Stopping Time of a c-Sample Rank-Order Sequential
Probability Ratio Test. vol.B
0 • 0 0 0 0 •••• 0 0 • 0 • 0 0 0 •• 0 • 0
Grimmett Go: Random Graph Theorems. . . . 203
0 0 0 0 • • 0 • • 0 • 0
rycaK,ll;. B.: Pacnpe,Il;erreHHe a6corrlOTHoro MaKcHM)'Ma nyaccoHoBCKHX H BH-
HepoBcKHX npou;eccoB Ha u;enH Map!('oBa . . . . 211
0 0 0 • • • • • 0 • 0
6
Guttman 1., Dutter R.: A Bayesian Approach to the Detection of Spurious
ness and Estimation in the General Univariate Linear Model when Outliers
are Present . . . . . . . . . . . . . vol. B
0 • • • • • • • • • • • • • •
Hampel Fo R.: Rejection Rules and Robust Estimates of Location: an Analysis
of Some Monte Carlo Results . . . . . . . . . . . . . . . . vol. B
0 • • •
Hartler G.: A Rough Test for Multivariate Independence ........ vol.B
Havranek T.: Some Aspects of Automatic Systems of Statistical Inference. 221
Hensz E., Jajte R.: Random Measures of Gleason Type. . . . . . . .. 231
Hida To: Functionals of Brownian Motion . . . . . . . . . . . . .. 239
Hinderer K., Hubner G.: An Improvement of J. F. Shapiro's Turnpike
Theorem for the Horizon of Finite Stage Discrete Dynamic Programs. . . 245
Hubner G.: Improved Procedures for Eliminating SUboptimal Actions in
Markov Programming by the Use of Contraction Properties . . . . . . . 257
Idzik A.: On Markov Policies in Continuous Time Discounted Dynamic
Programming . . . . 265
0 • 0 • • • • • • • • • • 0 • 0 • • •
Ihara S.: Coding Theory in Gaussian Channel with Feedback. . . . . . . vol.B
Imhof Jo P.: Oscillations of Monotone Amplitude and Application 277
0 •••
Ide A., Schmitz N.: Decision Theory for Continuous Observations I: Bayes
Solutions . . . . . . . . . . . . . . . . . . . . . . vol. B
0 ••••
Jilek M.: A Note on the Generalized Gamma Distribution: the Statistic
U = (X - y)/(X + Y) .............. 0 .. 0... 309
Jilovec S.: Uniformly Consistent Estimates ....... o. .. vol.B
0 •
Jureckova J.: Asymptotic Relations of Least-Squares Estimate and of Two
Robust Estimates of Regression Paratneter Vector .. vol.B
0 ••••• 0 • 0
Kaiikova V.: Optimum Solution of a Stochastic Optimization Problem with
Unknown Parameters. vol. B
0 • • • • • • • • • 0 • • • • • • • • • 0 • •
Kannappan PI.: An Axiomatic Characterization of the Measure Generalized
Directed Divergence . . . . . . . . . . . . . . . . . . . . . . . . vol. B
Kannappan PI., Rathie P. N.: On a Generalized Directed Divergence and
Related Measures. . . . . . . . . . . . . . . . . . . . . . . . vol. B
0 •
Kanter M.: On the Boundedness of Stable Processes. . . . . . . . . . . 317
KeMne <1>., AJIl,6epeH~T H.: 3KcTpanorur:QHH H ~eHTH4>HKa:qHH c.rryqaHHbIX
npon;eccoB Ha OCHOBe BeKTOpHbIX MapKoBCKHX MO~eJIeH ......... vol.B
Kligiene N.: On the Estimation of the Change Point in the Autoregressive
Sequence . . . . . . . 325
0 • • • • • • • • 0 • • • • • • • • • • • •
Konig D., Jansen U.: Stochastic Processes and Properties of Invariance for
Queueing Systems with Speeds and Temporary Interruptions. . . . . . . 335
Kozek A.: A Construction of UMV Estimators and Some Problems of Partial
Differential Equations. . . . . . vol. B
0 • • • • • 0 • • • • • • • • • • •
Kramosil I.: Gentzen-Like Random Axiomatic Systems. . . . . . . . . 345
Krishnaiah P. R., Schuurmann F. J.: Approximations to the Traces of
Complex Multivariate Beta and F Matrices .............. vol.B
7
Kubat L.: On Diagonstic Methods for Multi-Level Classification of Operation
of Technical Systems . . . . . . . . . . . . . . . . . . . . . . . . vol. B
Lanke J.: Asymptotic Normality in Simple Random Sampling ....... vol.B
Le Breton A.: Parameter Estimation in a Linear Stochastic Differential
Equation . . . . . . . . . . . . . . . . . . . . . . . . . . .. 353
Lee L., Thompson W. A., Jr.: Reliability of Multiple Component Systems .. vol.B
neoHoB IO. II.: Pacnpe.n:eJIeHHe BepoHTHocTeii nma CR . . . . . . .. 367
Liese F.: Charakterisierung einer Klasse von Entropiemaximalfolgen .... vol.B
Macchi 0.: The Fermion Process - a Model of Stochastic Point Process with
Repulsive Points . . . . . . . . . . . . . . . . . . . . . . . . . . 391
MareS M.: Competitive Equilibrium in a Market with Limited Cooperation. 411
Marosi J., Tusnady G.: On the Constructions of Confidence Intervals for the
Expectation of a Poisson Distribution on the Basis of Censored Data. . . vo1. B
Mathai A. M.: An Axiomatic Foundation for the Multivariate Measure of
Affinity with Applications in Social Statistics. . . . . . . . . . . . . . vo1. B
Michalek J.: Second Order Stochastic Processes and Self-Adjoint Operators. 433
Mihoc I.: On Measures of Information . . . . . . . . . . . . vol. B
Mikiewicz J.: Statistical Selection Method of the Best Objects . vol.B
Mollison D.: The Velocity of Stochastic Processes. . . . . . 441
N asell I.: A Mathematical Model of Helminthiasis with External Infection. 451
Nemetz T.: On a Finite Decision Model . . . . . . . . . . . . . . . . vol.B
Nollau V.: Zur operatorentheoretischen Charakterisierung symmetrisch
stabiler Prozesse . . . . . . . . . . . . . . . . . . . . . . . . . . 461
()sterreicher F.: On the Existence of Least Favourable Pairs of Distributions vo1.B
Pazman A.: A Contribution to the Time Series Design Problems. . . . . . 467
Piccinato L.: Predictive Distributions and Noninformative Priors ..... vo1.B
Plachky D.: A Characterization of Bounded Completeness in the Undo-
minated Case . . . . . . . . . . . . . . • . . . . . . . . . . . . 477
Plackett R. L.: The Information in Marginal Totals ........... vol.B
Pop-Stojanovic Z. R.: Continuous Filtering Problem for Ito-McShane
Stochastic Differential Equation . . . . . . . . . . . . . . . . . . . 481
Potschke D.: A Statistical Interpretation of the B-Rate ofInformation Theory vol.B
Radcliffe J.: Host-Vector Epidemics. . . . . . . . . . . . . . 489
Raudys S.: On the Accuracy of Some Estimates of Multivariate Density
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vol. B
Richardson D.: Replication and Stochastic Processes in Space . . 499
Rootzen H.: Renyi-Mixing and Functional Limit Theorems for Martingales 505
Rukhin A. L.: On the Estimation of a Transformation Parameter of a Distri-
bution Given on a Finite Group . . .............. vol.B
Rtischendorf L.: On One-Sample Rank Order Statistics for Dependent
Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . vol. B
Rusu I., Cotiu F.: Sur un probleme de programmation lineaire stochastique . vol.B
8
Saleh A. K. Md. E.: Behrens-Fisher Problem for the Exponential Distribution
in Censored and Uncensored Samples ................. vol.B
Sayed Y., Bogr J.: Measurement of Doppler Signals with Gaussian Spectra
Using Phase-Locked Loop ..................... vol.B
S chI e e W.: Asymptotische Verteilung des Kolmo goroff-Mehrstichproben-Tests
bei unstetiger Verteilungsfunktion. . . . . . . . . . . . . . . . . . . vol. B
Sendler W.: On the Moments of a Certain Class of Random Permanents. . 515
Shahani A. K.: A Trichotomous Process with Applications in Quality Control vol. B
Shpilewski E.: Estimation of the Parameters and Recognition of Stochastic
Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
Sibson R.: Distance Distributions . . . . . . . . . . . . . . . . . . . 527
Skala H. J.: Not Necessarily Additive Realizations of Comparative Probability
Relations - a Basis of Decision Theory ............... 545
Sladky K.: On the Optimality Conditions for Semi-Markov Decision Processes 555
Strei t F.: On Generalized Inverse Matrices and Multivariate Statistical
Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . vol. B
Szekely G. J.: The Brownian Taboo Bridge with an Application in the Theory
of Nonparametric Statistics . . . . . . . . . . . . . . . . . . .. 563
Thyregod P.: On Bayes Decision Rules for Symmetric Finite Populations .. vol.B
Vizkova Z.: A Local Limit Theorem for Dwass Statistic ......... vol.B
Watanabe S.: MOSS - a Subspace Representation of Classes in Pattern
Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . vol. B
W eron A.: Stochastic Processes of Second Order with Values in Banach Spaces 567
Wessels J.: Stopping Times and Markov Programming. . . . . . . . 575
Winkelbauer K.: Information Channels with Memoryless Components . vol.B
Yeo G.: Dams with Variable Release Rates. . . . . . . . . . . . . 587
Zelinski R.: A Randomized Kiefer-Wolfowitz Procedure. . . . . .. . vol.B
Ziezold H.: On Expected Figures and a Strong Law of Large Numbers for
Random Elements in Quasi-Metric Spaces. . . . . . . . . . . . . .. 591
9
PREFACE
The Prague Conferences on Information Theory, Statistical Decision Functions, and
Random Processes have been organized every three years since 1956. During the
eighteen years of their existence the Prague Conferences developed from a platform
for presenting results obtained by a small group of researchers into a probabilistic
congress, this being documented by the increasing number of participants as well as
of presented papers.
The importance of the Seventh Prague Conference has been emphasized by the
fact that this Conference was held jointly with the eighth European Meeting of
Statisticians. This joint meeting was held from August 18 to 23, 1974 at the Technical
University of Prague. The Conference was organized by the Institute of Information
Theory and Automation of the Czechoslovak Academy of Sciences and was sponsored
by the Czechoslovak Academy of Sciences, by the Committee for the European
Region of the Institute of Mathematical Statistics, and by the International As
sociation for Statistics in Physical Sciences.
More than 300 specialists from 25 countries participated in the Conference.
In 57 sessions 164 papers (including 17 invited papers) were read, 128 of which are
published in the present two volumes of the Transactions of the Conference. Volume
A includes papers related mainly to probability theory and stochastic processes,
whereas the papers of Volume B concern mainly statistics and information theory.
It gives us a pleasure to express our gratitude to all who have contributed to the
success of the Conference, especially to the sponsoring institutions and their repre
sentatives, and to those who read papers and delivered their manuscripts for publi
cation in the Transactions.
Sincere thanks are due to Academician Jaroslav Kozesnik, the scientific editor
of these volumes, to the editorial board the members of which read all published
manuscripts, and also to all employees of the Institute of Information Theory and
Automation who participated in the organization of the Conference.
The Organizing Committee is very sorry that the premature death of two of its
members, who participated in the preparation of this volume, prevented them from
seeing the fruits of their labour. Ing. Libor Kubat died on 28th December, 1975,
at the age of fourty-six and Dr. Zdenek Koutsky died on 3rd June, 1976, at the age
of fifty-two. Ing. Kubat, as the executive editor, and Dr. Koutsky, as one of the main
organizers, contributed invaluably to the success of this Conference, as well as of all
our previous conferences. The function of the executive editor of this volume was
assumed by Dr. Milan Ullrich.
ORGANIZING COMMITTEE
11