BOOK REVIEWS

Book reviewed in this article:
Finney, D. J. Statistics for Mathematicians. An Introduction. Oliver and Boyd
Hadley, G. Introduction to Probability and Statistical Decision Theory. Holden-Day
Johnson, N. L., and Leone, F. C. Statistics and Experimental Design in Engineering and the Physical Sciences.
Benjamin, B. Health and Vital Statistics.
Bhat, U. N. A Study of the Queueing Systems M/G/1 and GI/M/1. (Lecture Notes on Operations Research and Mathematical Economics.)     

Reviews

Books reviewed in this issue.
What Is a Number? Mathematical Concepts and Their Origins
Robert Tubbs
Infectious Diseases: a Geographical Analysis. Emergence and Re-Emergence
A. D. Cliff, M. R. Smallman-Raynor, P. Haggett, D. F. Stroup and S. B. Thacker
"Sleepwalking to Segregation"? Challenging Myths about Race and Migration
Nissa Finney and Ludi Simpson
Failing to Figure: Whitehall's Costly Neglect of Statistical Reasoning
Mervyn Stone (with a Foreword by Dennis V. Lindley)
Advances in Telephone Survey Methodology
J. M. Lepkowski, C. Tucker, J. M. Brick, E. D. de Leeuw, L. Japac, P. J. Lavrakas, M. W. Link and R. L. Sangster (eds)     

BOOK REVIEWS

Book reviewed in this article:
Draper, N., and Smith, H. Applied Regression Analysis. John Wiley & Sons.
Deutsch, R. Estimation Theory
Margaris, Angelo. First Order Mathematical Logic.
Chakravarti, I. M., Laha, R.G. and Roy, J. Handbook of Methods of Applied Statistics.
Cunningham, K. S. The Social Bcience Research Council of Australia
Martin, J. J. Bayesian Decision Problems and Markou Chains
Hillier, Frederick S., and Lieberman, Gerald J. Introduction to Operations Research
Campbell, R. C. 8tatistics for Biologists
Rozanov, Yu. A. Etationary Random Processes
Bliss, C. I. Statistics in Biology
Ferguson, Thomas S. fiIathematical atatistics: A Decision Theoretic Approach
Kingman, J. F. C., and Taylor, S. J. Introductiota to Measure and Probability
Simonnard, M. Linear Programming     

Book Reviews

Book reviewed in this article:
De Haan, L. On Regular Variation, and Its Applications to the Weak Convergence of Sample Extremes. Mathematical Centre Tracts No. 32
Johnson, N. L., and Kotz, S. Distributions in Statistics: Continuous Univariate Distributions.
Joiner, Brian L., Laubscher, N. F., Brown, Eleanor S., and Levy, Bert. An Author and Permuted Title Index to Selected Statistical Journals.
Kendall, M. G. Bank Correlation Methods. 4th edition
Lass, H., and Gottlieb, P. Probability and Statistics.
Neveu, J. Bases Mathematiques du Caleul des Probabilites.
Maddox, I. J. Elements of Functional Analysis.
Aitchison, John. Choice Against Chance: An Introduction to Statistical Decision Theory.
Chat field, C. Statistics for Technology.
Cramer, H. Random Variables and Probability Distributions. Third edition
Feller, William (1966). An Introduction to Probability Theory and Its Application.
De Leve, G., Tijms, H. C, and Weeda, P. J. Generalized MarTcovian Decision Processes (Applications).
Hajek, J. Nonparametric Statistics.
Hinderer, K. Foundations of Non-stationary Dynamic Programming with Discrete Time Parameter.
Kreyszig, E. Introductory Mathematical Statistics. Principles and Methods.
Patil, G. P. (Editor). Random Counts in Models and Structures.
Pearson, E. S., and Kendall, M. G. (Editors). Studies in the History of Statistics and Probability.
Puri, M. L. (Editor). Nonparametric Techniques in Statistical Inference.
Yates, Frank. Experimental Design—Selected Papers.     

BOOK REVIEWS

Book reviewed in this article:
Neveu, J. Martingales a Temps Discret.
Roussas, George G. A First Course in Mathematical Statistics.
Nelson, C. R. Applied Time Series Analysis for Managerial Forecasting.
Larson, Harold J. Introduction to the Theory of Statistics.
Seber, G. A. F. The Estimation of Animal Abundance and Belated Parameters.
Som, R. K. A Manual of Sampling Techniques.
Haitovsky, Y. Regression Estimation from Grouped Observations.
Kendall, M. G. Time Series Analysis.
Freedman, D. Approximating Countable Markov Chains.
Lewis, P. A. W. (Ed.). Stochastic Point Processes: Statistical Analysis, Theory and Applications.
Edwards, A. W. F. Likelihood. An Account of the Statistical Concept of Likelihood and its Application to Scientific Inference.
Barnett, V. Comparative Statistical Inference.
Taylor, S. J. Introduction to Measure and Integration.     

Book Reviews

Books reviewed in this article:
Sheldon M. Ross, An Introduction to Mathematical Finance: Options and Other Topics
James Franklin, The Science of Conjecture: Evidence and Probability before Pascal     

BOOK REVIEWS

Book reviewed in this article:
Concepts of Nonparametric Theory. By John W. Pratt and Jean D. Gibbons.
Point Processes and Queues. Martingale Dynamics. By P. Brémaud.
Statistical Models and Methods for Lifetime Data. By J. F. Lawless.
An Introduction to Stochastic Processes and Their Applications. By C. L. Chiang.
Recent Advances in Regression Methods. By Hrishikesh D. Vinod and Aman Ullah.
Topics in Applied Multivariate Analysis. Edited by D. M. Hawkins.
Time Series Analysis: Theory and Practice 1. Proceedings of the International Conference held at Valencia, Spain, June 1981. Edited by O. D. Anderson (in collaboration with J. E. De Gooijer and K. D. S. Stoodley).
Seminar on Stochastic Processes, 1981. Edited by E. Çinlar, K. L. Chung and R. K. Getoor.
Probability and Statistical Inference. Proceedings of the Second Pannonian Symposium on Mathematical Statistics, Bad Tatzmannsdorf, Austria, 1981. Edited by W. Grossman, G.Ch. Pflug and W. Wertz. Dordrecht: D. Reidel.
Some Recent Advances in Statistics. Edited by J. Tiago de Oliveira and Benjamin Epstein.
Stochastic Monotonicity and Queueing Applications of Birth-Death Processes. By Erik van Doorn. (Lecture Notes in Statistics, Vol. 4)
Statistical Distributions in Scientific Work. Edited by C. Taillie, G. P. Patil & B. A. Baldessari.
Identification and Informative Sample Size. By H. H. Tigelaar.
Statistics Without Tears. By Derek Rowntree.
The Mathematical Theory of the Dynamics of Biological Populations II. Edited by R. W. Hiorns & D. Cooke.     

Book Notices

Mathematical Models for the Growth of Human Populations. By J. H. Pollard
Approximate Behavior of Tandem Queues. By G. F. Newell. Berlin: Springer
A Primer in Probability. By Kathleen Subrahmaniam
Random Processes: A First Look. By R. Syskí. New York: Marcel Dekker
Collecting Sensitive Data by Randomized Response: An Annotated Bibliography. By W. W. Daniel
Graph Theory and Combinatorics.Edited by R. J. Wilson     

Book Reviews

Book reviewed in this article:
Random Coefficient Autoregressive Models: An Introduction. : By Des F. Nicholls & Barry G. Quinn.
Neyman-From Life. By Constance Reid.
Tests for Preference. By J. J. Dik.
Higher Order Asymptotics for Simple Linear Rank Statistics. Mathematical Centre Tracts 151.
Reliability in the Acquisitions Processes. By Douglas J. De Priest and Robert L. Launer (Eds).     

BOOK REVIEWS

Book reviewed in this article:
Real Variable. By J. M. Hyslop.
Basic Mathematics for Students of Economics. By R. S. G. Rutherford
Kendall, Maurice G., and Buckland, William R. A Dictionery of Statistical Terms.
Kendall, Maurice G., and Buckland, William R. A Dictionery of Statistical Terms—Supplement
Pearson, K. Mathematical Contributions to the Theory of Evolution.     

BOOK REVIEWS

Book reviewed in this article:
Smith, W. L., and Wilkinson, J. H. (Editors). Proceedings of the Symposium on Congestion Theory, held at the University of North Carolina 1964.
Rao, C. R. (Editor). Contributionns to Statistics
Kendall, M. G., and Doig, Alison G. Bibliography of Statistical Literature, 1940–1949 Oliver & Boyd.
Guttman, I., and Wilks, S. S. Introductory Engineering Statistios.
Brunk, H. D. An Introduction to Mathematical Statistics.
Wetherill, G. Barrie. Sequential Metho& in Statistics.
Neveu, J. Mathematical Foundations of the Calculus of Probability.
Skorokhod, A. V. Studies in the Theory of Random Processes.
Goodwin, Crawford D. W. Economic Enquiry in Australia.
Krickeberg, K. Probability Theory.     

BOOK REVIEWS

Book reviewed in this article:
Seneta, E. Regularly Varying Functions. Springer Lecture Notes in Mathematics No. 508. Springer-Verlag
Statistical Quality Control Methods. Marcel Dekker Inc., Few York and Basel
The Mathematical Theory of Infectious Diseases and its Applications. Griffin, London
Statistical Quality Control Metho&. Marcel Dekker Inc., New Pork and Basel
Variational Methods in Statistics. Academic Press, New York
Perspectives in Probability and Statistics. Papers in honour of M. S. Bartlett on theoccasion of his sixty-fifth birthday. Academic Press, London
Stochastic Processes and Related Topics (1). Statistical Inference and Belated Topics(2). Academic Press, Inc. New York
Mathai, A. M. and Rathie, P. N. Basic Concepts in Information Theory and Statistics. Wiley Eastern Limited, New Delhi
Banerjee, K. S. Cost of Living Index Numbers: Practice, Precision and Theory. Marcel Dekker Inc., New York
Kahn, P. M. (Ed.).Credibility: Theory and Applications. Academic Press, New York
Kendall, Sir Maurice Multivariate Analysis. Charles Griffin and Company Ltd     

BOOK REVIEWS

Book reviewed in this article:
Rall, Louis B. Computational Solution of Nonlinear Operator Equations.
Hodges, J. L., and Lehmann, E. L. Basic Concepts of Probability alzd Statistics.
Hope, Keith. Methods of Multivariate Analysis.
Heritage, Raymond S. Learning Decimal Currency. Penguin Books, Middlesex.
Wasan, M. T. Stochastic Approx%mation.
Larson, Harold J. Introduction to Probability Theory and Statistical Inference.
Anderssen, R. S., and Osborne, M. R. (Editors). Least Squares Methods in Data Analysis.
Elderton, W. P., and Johnson, N. L. Systems of Frequency Curves.
Billingsley, P. Convergence of Probability Neasuree.
Moore, P. G. Principles of Statistical Techniques. Second Edition.
Craddock, J. M. Statistics in the Computer Age.
Lukacs, E. Stochastic Converaence. Heath Mathematical Mono-graphs, Heath, Lexington, Mass.
Khinchin, A. Ya. The Teaching of Mathematics. Edited by B. V. Gnedenko.     

Stable estimation of location parameter -nonasymptotic approach

Let X₁:, X₂:, …, X_n be iidrv's with cdf F?, F?(x)=F (x-θ), R. Let T be an equivariant median-unbiased estimator of θ. Let πε(F)={G = (1 -ε) F+εH, H any cdf} and let M(G, T) be a median of T if X₁ has cdf G. The oscillation of the bias of T, defined as

Bε(T)=sup (M(G₁ T) :G₁,G₂:∈π_σ:(F)} ,is considered and the estimator with the smallest B$epsi;(T) is explicitly constructed     

Book Reviews

Books reviewed:
Anthony, Atkinson & Marco, Riani, Robust Diagnostic Regression Analysis
N., Balakrishnan & C.R., Rao, Order Statistics: Theory & Methods. Handbook of Statistics, Volume 16
N., Balakrishnan & C.R., Rao, Order Statistics: Applications. Handbook of Statistics, Volume 17
C.R., Rao & G.J., Székely, Statistics for the 21st Century: Methodologies for Applications of the Future
D.A., Nolan & T.P., Speed, Stat Labs: Mathematical Statistics Through Applications
W.N., Venables & B.D., Ripley, S Programming
Peter W.M., John, Statistical Design and Analysis of Experiments     

Book review

G.Bamberg:Statistische Entseheldungstheorle, Physica-Verlag, Würzburg-Wien 1972, 149 S., DM 20,–.

J.M.Mendel:Discrete Techniques of Parameter Estimation. Marcel Dekker, Inc., New York 1973, XIV, 385 S., $ 19.50.

P.Eykhoff:System Identification. Parameter and State Estimation. John Wiley & Sons, London 1974, XX, 555 pp., £ 12.50.

G.Härtler:Versuchsplanung und Statistische Datenanalyse, Akademie-Verlag, Berlin 1976, 103 S., 6 Abb., 12,– M.

P.Mertens(Hrsg.):Prognoserechnung. Physica-Verlag, Würzburg-Wien 1973; 295 S., DM 48,–

E.Schaich, D. Kohle, W.Schweitzer, F.Wegner:Statistik I (für Volkswirte, Betriebswirte und Soziologen.) Verlag Franz Vahlen GrnbH, München 1974, 160 S., DM 22,80.

A.Rosengard: Probabilltés et Statistique en Recherche Scientifique. Dunod, Paris 1972, XIV, 310 S.

D. Zschocke:Betriebsökonometrie.Physica-Verlag, Würzburg-Wien 1974, 287 S., DM 90.–.

J.C.G. Boot, E.B. Cox:Statistical Analysis for Managerial Decisions. McGraw-Hill, Inc., New York 1970, XI, 651 S.

H.Richter, V. Mammitzsch: Methode der kleinsten Quallrate (mit Übungen und Aufgaben).Verlag Berliner Union GmbH, Stuttgart, und Verlag W. Kohlharnmer GmbH, Stuttgart-Berlin-Köln-Mainz 1973, 144 S., DM 24,–.

O.Anderson, W. Popp, M. Schaffranek, D. Steinmetz, H. Stenger: Schätzen und Testen. Eine Einfhrung in die Wahrscheinlichkeitsrechnung und schließeude Statistik.Springer-Verlag, Berlin-Heidelberg-New York 1976, XI, 385 S., 68 Abb., 56 Tab., DM 19,80.

H.Bauer:Wahrscheinlichkeitstheorie und Grundzilge der Maßtheorie. Walter de Gruyter, Berlin-New York 1974, 407 S., DM 48,–.

A.M.Mathai, P.N. Rathie:Basic Concepts in Information and Statistics(Axioluatic Foundations and Applications). Wiley Eastern Limited, New Delhi 1975, X, 137 S., £ 2.75; $ 5.50.

D.F.Merriam (Hrsg.): Random Processes in Geology.Springer-Verlag, Berlin-Heidelberg-New York 1976, VIII, 168 S., 63 Abb., 18 Tab., DM 34,50.

G.Matheron: Random Sets and Integral Geometry. Wiley Series in Probability and Mathematical Statistics, J. Wiley and Sons, New York 1975, XXIII, 261 S., £ 10.60; $ 21.20.

L.Kleinrock: Queueing Systems. Volume I: Theory. J. Wiley and Sons, New York-London-Sydney-Toronto 1975, XVIII, 417 S.; £ 13.55; $ 24.30.

Bartsch, H.-J.:Mathematische Formeln, VEB Fachbuchverlag, Leipzig 1976,15. Auflage, 510 S., 362 Abb., 9,80 M.     

Books Reviews

Statistical Analysis of Finite Mixture Distributions. By D. M. Titterington, A. F. M. Smith & U. E. Makov
Plots, Transformations, and Regression: an Introduction to Graphical Methods of Diagnostic Regression Analysis. By A. C. Atkinson.     

Convergence rates in the law of large numbers for END linear processes with random coefficients

Abstract

In this paper, we consider convergence rates in the Marcinkiewicz–Zygmund law of the large numbers for the END linear processes with random coefficients. We extend some results of Baum and Katz (1965 Baum, L. E., and M. Katz. 1965. Convergence rates in the law of large numbers. Transactions of the American Mathematical Society 120 (1):108–23. doi: 10.2307/1994170.[Crossref], [Web of Science ®] , [Google Scholar]) to the case of dependent linear processes with the random coefficients.     

Effectiveness of combinations of Gaussian graphical models for model building

Combining statistical models is an useful approach in all the research area where a global picture of the problem needs to be constructed by binding together evidence from different sources [M.S. Massa and S.L. Lauritzen Combining Statistical Models, M. Viana and H. Wynn, eds., American Mathematical Society, Providence, RI, 2010, pp. 239–259]. In this paper, we investigate the effectiveness of combining a fixed number of Gaussian graphical models respecting some consistency assumptions in problems of model building. In particular, we use the meta-Markov combination of Gaussian graphical models as detailed in Massa and Lauritzen and compare model selection results obtained by combining selections over smaller sets of variables with selection results over all variables of interest. In order to do so, we carry out some simulation studies in which different criteria are considered for the selection procedures. We conclude that the combination performs, generally, better than global estimation, is computationally simpler by virtue of having fewer and simpler models to work on, and has an intuitive appeal to a wide variety of contexts.     

Book Reviews

Book reviewed in this article:
Van Wijngaarden, A. (Editor). Report on the Algorithmic Language ALGOL 68. Second printing by the Mathematisch Centrum, Amsterdam, ME101
David, F. N., Barton, D. E., Ganeshalingam, S., Harter, H. L., Kim, P. J., Merrington, M., and Walley, D. Normal Centroids, Medians and Scores for Ordinal Data. Series: Tracts for Computers
Hadley, G. Elementary Statistics
Hultquist, Robert A. Introduction to Statistics
Haber, A., and Runyon, R. P. General Statistics
Sachs, L. Statistische Auswertungsmethoden. Second edition
Johnson, N. L., and Kotz, S. Distributions in Statistics: Discrete Distributions
Anderssen, R. S., and Osborne, M. R. (Editors). Data Representation
Zuwaylif, F. H. General Applied Statistics
Schmitt, S. A. Measuring Uncertainty: An Elementary Introduction to Bayesian Statistics
Breipohl, A. M. Probabilistic Systems Analysis
Larson, H. J. Introduction to Probability Theory and Statistical Inference
Klugh, Henry E. Statistics: The Essentials for Research
Mosteller, F., Bush, R. R., and Green, B. F. Selected Quantitative Techniques and Attitude Measurement
Harnett, D. L. Introduction to Statistical Methods
Krutchkoff, R. G. Probability and Statistical Inference
Haber, A., Runyon, R. P., and Badia, P. Readings in Statistics
Milton, R. C. Bank Order Probabilities: Two Sample Normal Shift Alternatives