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 REVIEWS

Book reviewed in this article:
Hannan, E. J. Multiple Time Series.
Bancroft, T. A., and Brown S. A. Statistical Papers in Honour of George W. Snedecor.
Friedman, A. Differential Games
Henderson, Ronald F., Harcourt, Alison, Harper, R. J. A., and Shaver, Sheila. The Melbourne Poverty Survey: Further Notes on Methods and Results .
Lukacs, Eugene. Characteristic Functions
Searle, S. R. Linear Models     

Robust estimation in long-memory processes under additive outliers

In this paper, we introduce an alternative semiparametric estimator of the fractional differencing parameter in ARFIMA models which is robust against additive outliers. The proposed estimator is a variant of the GPH estimator [Geweke, J., Porter-Hudak, S., 1983. The estimation and application of long memory time series model. Journal of Time Series Analysis 4, 221–238]. In particular, we use the robust sample autocorrelations of Ma, Y. and Genton, M. [2000. Highly robust estimation of the autocovariance function. Journal of Time Series Analysis 21, 663–684] to obtain an estimator for the spectral density of the process. Numerical results show that the estimator we propose for the differencing parameter is robust when the data contain additive outliers.     

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.     

Reviews

Andersen, P. K., Borgan, O., Gill, R. D. and Keiding, N. Statistical Models based on Counting Processes
Anderson, T. W. and Finn, J. D. The New Statistical Analysis of Data
Azzalini, A. Statistical Inference—based on the Likelihood
Borodin, A. N. and Salminen, P. Handbook of Brownian Motion—Facts and Formulae
Brockwell, P. J. and Davis, R. A. Introduction to Time Series and Forecasting
Chapman, M. and Wykes, C. Plain Figures
Clarke, G. M. and Kempson, R. E. Introduction to the Design and Analysis of Experiments
Goldstein, H. and Lewis, T. (eds) Assessment: Problems, Developments and Statistical Issues; a Volume of Expert Contributions
Grenander, U. Elements of Pattern Theory
Högnäs, G. and Mukherjea, A. Probability Measures on Semigroups
Levitas, R. and Guy, W. Interpreting Official Statistics
van der Linden, W. J. and Hambleton, R. K. (eds) Handbook of Modern Item Response Theory
Ross, S. M. Simulation
Simonnet, M. Measures and Probabilities
Small, C. G. The Statistical Theory of Shape
van der Vaart, A. and Wellner, J. A. Weak Convergence and Empirical Processes with Applications to Statistics     

Book Reviews

Book reviewed in this article:
Martingale Limit Theory and its Application . By P. Hall and C. C. Heyde.
The Geometry of Random Fields . By Robert J. Adler. Chichester: John Wiley.
Finite Mixture Distriiutions . By B. S. Everitt and D. J. Hand
Time Series Models . By A. C. Harvey.
Statistics for Biologists . By D. J. Finney.
Intermediate Statistical Methods. By G. B. Wetherill.
Statistical Methods in Cancer Research. Vol. 1. The Analysis of Case-Control Studies. By N. E. Breslow and N. E. Day.
Sampling Methods for Censuses and Surveys. By Frank Yates, F.R.S. High Wycombe: Griffin.
Statistical Theory of Sampling Inspection by Atbniutes. By A. Hald.
Time Series Analysis. Edited by 0. D. Anderson and M. R. Perryman.
Bayesian Statistics. Proceedings of the First International Meeting held in Valencia (Spain), May 28 to June 2, 1979. Edited by J. M. Bernardo, M. H. De Groot, D. V. Lindley and A. F. M. Smith.
The Theory and Practice of Econometrics. By George G. Judge, WiUiam E. Griffths, R. Carter Hill and Tsoung-Chao Lee.
Social Measurement and Social Indicators: Issues of Policy and Theory. By Michael Carley.
Multiple Attriiute Decision Making. By Ching-Lai Hwang and Kwangsun Yoon. Berlin, Heidelberg, New York. Springer-Verlag.
Characterization of Optimal Strategies in Dynamic Games. By L. P. J. Groenewegen.
Redundancy and Linear Programs. By J. Telgen.
Matrix Derivatives. By Gerald S. Rogers.     

Book reviews

Donald J. Koosis: Statistics. A Self-Teaching Guide, Fourth Edition. Wiley 1997, ISBN 0-471-14688-9

Christopher C. Heyde: Quasi-Likelihood and Its Applications, Springer Series in Statistics, 1997, pp. 235, [ISBN 0-387-98225-61

Jeffrey S. Simonoff: Smoothing Methods in Statistics, Springer Series in Statistics, 1996, pp. 338

Andr´e I. Khuri, Thomas Mathew and Birmal K. Sinha: Statistical Tests for Mixed Linear Models, Wiley Series in Probability and Statistics, 1998, pp. 352, PSBN 0-471-1 5653-11

Ronald Christensen: Log-Linear Models and Logistic Regression, Springer Texts in Statistics, 1997, pp. 483, [ISBN 0-387-98247-71

E. L. Lehmann: Testing Statistical Hypotheses, Springer Texts in Statistics, 1997, pp. 600, [ISBN 0-387-94919-41

S. R. Searle, G. Casella and Ch. E. McCulloch: Variance Components, Wiley and Sons, 1992, pp. 496, [ISBN 0-471-62162-51

B. J. T. Morgan: Analysis of Quantal Response Data, Chapman & Hall, 1992, pp. 51 1

Carl D. Huberty: Applied Discriminant Analysis, Wiley and Sons, 1994, pp. 490

C. R. Rao and H. Toutenburg: Linear Models. Least Squares and Alternatives, Springer Series in Statistics, 1995, 188 pp., [ISBN 0-387-94562-81     

Book Reviews

Book reviewed in this article:
An Introduction to Bispectral Analysis and Bilinear Time Series Models. By T. Subba Rao and M. M. Gabr.
Probability. By A. N. Shiryayev.
An Introduction to Latent Variable Models. By B. S. Everitt.     

BOOK REVIEWS

Book reviewed in this article:
Cox, D. R., and Lewis, P. A. W. The Statistical Analysis of Series of Events.
Rao, C. Radhakrishna. Linear Statistical Inference and Its Applications.
Bennett, B. M., and Horst, C. Supplement to Tables for Testing Significance in a 2 × 2 Contingency Table.
Huitson, A. The Analysis of Variance.
Moran, P. A. P., and Smith, C. A. B. The Correlation between Relatives on the Supposition of Mendelian Inheritance.
Searle, S. R. Matrix Algebra for the Biological Sciences.
Feller, W. An Introduction to Probability Theory and Its Applications.
Ashton, Winifred D. The Theory of Road Traffic Flow.
Kemeny, J. G., Snell, J. L., and Thompson, G. L. Introduction to Finite Mathematics.
Coale, A. J., and Demeny, P. Regional Model Life Tables and Stable Populations.     

Automatic Block-Length Selection for the Dependent Bootstrap

We review the different block bootstrap methods for time series, and present them in a unified framework. We then revisit a recent result of Lahiri [Lahiri, S. N. (1999b). Theoretical comparisons of block bootstrap methods, Ann. Statist. 27:386-404] comparing the different methods and give a corrected bound on their asymptotic relative efficiency; we also introduce a new notion of finite-sample “attainable” relative efficiency. Finally, based on the notion of spectral estimation via the flat-top lag-windows of Politis and Romano [Politis, D. N., Romano, J. P. (1995). Bias-corrected nonparametric spectral estimation. J. Time Series Anal. 16:67-103], we propose practically useful estimators of the optimal block size for the aforementioned block bootstrap methods. Our estimators are characterized by the fastest possible rate of convergence which is adaptive on the strength of the correlation of the time series as measured by the correlogram.     

Book reviews

S.M.Kendall:Multivariate Analysis.Charles Griffin & Co. Ltd., London and High Wycombe 1975, 210 pp

C.T.Leondes (ed.):Control and Dynamic Systems, Advances in Theory and Applications. Vol. 11, Academic Press, New York and London 1974, 516 pp., $ 24.50.

CH. R.Nelson:Applied Time Series Analysis for Managerial Forecasting. Holden Day, Inc., San Francisco 1973, 231 pp., $ 14.95.

B.DE Finetti:Theory of Probability. Vol. 1, 2, John Wiley & Sons, New York, London, Sydney, Toronto. Vol. 1, 1974, 300 pp., £ 7.50 - Vol. 2 1975, 375 pp., £ 10.50.

P.Erdördos, J. Spencer:Probabilistic Methods in Combinatorics. Akadémic Press, New York and London; Akadémiai Kiadó, Budapest 1974, 106 pp., $ 11.75.

J.S.R.Ustagi:Variational Methods in Statistics.Academic Press, New York and London 1975.

J.S.Rustagi:Optimizing Methods in Statistics.Academic Press, New York and London 1971,488 pp., $ 17.00.

Karl V. Bury:Statistical Models in Applied Science. John Wiley & Sons, New York-London-Sydney-Toronto 1975,.625 pp., £ 15.60; $ 28.00.

Michael R. Anderberg:Cluster Analysis for Applications. Academic Press, New York-San Francisco-London 1973, 359 pp., $ 27,–.

J.L.Fleiss:Statistical Methods for Rates and Proportions. John Wiley & Sons, New York-London-Sydney-Toronto 1973. 223 pp., £ 6.50.

J.Tanur et al. (Ed.):Statistics:A Guide to the Unknown. Holden Day, Inc., San Francisco 1972, 430 pp.

H.VÁliaho, T. Pekkonen:A Procedure for Stepwise Regression Analysis.Akademie-Verlag, Berlin 1976, 90 pp., 18,– M.

M.Reinfeldt, U. TrÁnkle:Signifikanztabellen statistischer Testvertellungen. R. Oldenbourg Verlag, Mnchen, Wien 1976, 151 S., DM 44,–.

R.E.Barlow, D.J.Batholomew, J.M.Bremner, H.D.Brunk:Statistical Inference Under Order Restrictions.(The Theory and Applications of Isotonic Regression.) John Wiley & Sons, New York 1972, 388 pp., £ 7.50.

H.J.Larson:Introduction to Probability Theory and Statistical Inference. Wiley, New York 1974, 430 pp., £ 6.85.

R.A.Carlson:Statistics. Holden Day, Inc., San Francisco 1973, 393 pp.

E. Page:Queueing Theory in OR. Butterworths, London 1972, 187 pp., £ 3.60.

H.Krampe, J.Kubat, W.Runge:Bedienungsmodelle. Ein Leitfaden für die praktische Anwendung, Verlag Die Wirtachaft, Berlin 1973, 512 S., 79,– M.

G.S.Fishman:Concepts and Methods in Discrete Events Digital Simulation. John Wiley & Sons, New York 1973, 385 pp., £ 8,75.     

Automatic Block-Length Selection for the Dependent Bootstrap

Abstract

We review the different block bootstrap methods for time series, and present them in a unified framework. We then revisit a recent result of Lahiri [Lahiri, S. N. (1999b). Theoretical comparisons of block bootstrap methods, Ann. Statist. 27:386–404] comparing the different methods and give a corrected bound on their asymptotic relative efficiency; we also introduce a new notion of finite-sample “attainable” relative efficiency. Finally, based on the notion of spectral estimation via the flat-top lag-windows of Politis and Romano [Politis, D. N., Romano, J. P. (1995). Bias-corrected nonparametric spectral estimation. J. Time Series Anal. 16:67–103], we propose practically useful estimators of the optimal block size for the aforementioned block bootstrap methods. Our estimators are characterized by the fastest possible rate of convergence which is adaptive on the strength of the correlation of the time series as measured by the correlogram.     

Book Reviews

Book reviewed in this article:
The History of Statistics in the 17th and 18th Centuries Against the Background of Intellectual, Scientific and Religious Thought.
Brownian Motion and Classical Potential Theory.By S. C. Port and C. J. Stone
Probabilistic Analysis and Related Topics. Volume 1.Edited by A. T. Bharucha-Reid
Measure and Integral. By Konrad Jacobs
Bayesian Control of Markov Chains. By K. M. van Hee
Classifying Infinitely Divisible Distributions by Functional Equations. By K. van Harn
Interfaces between Computer Science and Operations Research. Edited by J. K. Lenstra, A. H. G. Rinnooy Kan, and P. van Emde Boas
Analysis of Economic Time Series. A Synthesis. By M. Nerlove, D. M. Grether and J. L. Carvalho
Principles of Statistical Inference (2nd edition). By P. G. Moore
Fixed Effects Analysis of Variance. By L. Fisher and J. M. McDonald
Analysis of Qualitative Data, Vol. 1. Introductory Topics. By Shelby J. Haberman
Statistical Services in Ten Years' Time. Edited by Joseph W. Duncan     

BOOK REVIEWS

Book reviewed in this article:
Incomplete Block Designs. By Peter W. M. John.
Statistical Modeling Techniques. By Samuel S. Shapiro and Alan J. Gross
Factorial Designs. By B. L. Raktoe, A. Hedayat and W. T. Federer.
Stochastic Storage Processes—Queues, Insurance Risk and Dams. By N. U. Prabhu.
A User's Guide to the Gottman-Williams Time Series Analysis Computer Programs for Social Scientists. By Esther A. Williams and John M. Gottman.
Statistics at Work. Edited by S. Gubbins, D. A. Rhoades, D. Vere-Jones.
Computing in Statistical Science through APL. By Francis John Anscombe.     

Book Reviews

Book reviewed in this article:
The Design and Analysis of Longitudinal Studies: By Harvey Goldstein.
R. A. Fisher: An Appreciation. Edited by S. E. Fienberg & D. V. Hinkley.
Measurement in the Social Sciences. By R. A. Zeller & E. G. Carmines.
Analysis with Standard Contagious Diptriiutions. By J. B. Douglas.
Comparison of Box-Jenkins and Bonn Monetary Model Prediction Performance. By M. N. Bhattacharyya.
The Econometric Analysis of Time Series. By A. C. Harvey.
Estimation of Density from Line Transect Sampling of Biological Populations. By K. P. Bumham, D. R. Anderson & J. L. Laake.
Multrvariate Analysis-V. Proceedings of the Fifth International Symposium on Multivariate Analysis. Edited by P. R. Krishnaiah.
Recent Developments in Statistical Inference and Data Analysis. Edited by K. Matusita.
Contributions to Statistics. Edited by J. Jurecková.     

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     

EM-based algorithms for autoregressive models with t-distributed innovations

This paper considers the estimation of parameters of AR(p) models for time series with t-distribution via EM-based algorithms. The paper develops asymptotic properties for the estimation to show that the estimators are efficient. Also testing theory for the estimators is considered. The robustness of the estimators and various tests to deviations from an assumed model is investigated. The study shows that the algorithms have equal estimation efficiency even if the error distribution is miss-specified or perturbed by outliers. Interestingly, the estimators from these algorithms performed better than that of the Modified Maximum Likelihood (MML) considered in Tiku et al. (2000 Tiku, M. L., Wong, W. K., Vaughan, D. C., Bian, G. (2000). Time series models in non-normal situations: Symmetric innovations. Journal of Time Series Analysis, 21: 571–596. [Google Scholar]).     

Book Reviews

Books reviewed:
Philip Hans Franses & Dick van Dijk, Non-linear Time Series Models in Empirical Finance
Herbert Spirer, Louise Spirer & A.J. Jaffe, Misused Statistics
Deborah J. Bennett, Randomness
C.E. Linneborg, Data Analysis by Resampling: Concepts and Applications
I. Clark and W.V. Harper, Practical Geostatistics 2000     

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.