Nonparametric Statistical Inference Research Articles

Nonparametric Statistical Inference, 2nd Edition.

Nonparametric Statistical Inference, 2nd Edition.

Nonparametric Statistical Inference. 2nd Edition.

Nonparametric Statistical Inference. 2nd Edition.

An associative hierarchical self-organizing system

A system that learns to predict events in various environments is described. The system is associative and distributed; a hierarchical self-organization of low-level units into high-level units takes place based on experience in a particular domain. Its design is inspired by widely held principles of brain organization and by some newly developed techniques in nonparametric statistical inference. The system can be regarded as a realization of a nonparametric statistical algorithm. This is demonstrated by a discussion of system architecture and a presentation of an application in a `number theory' environment.

Isomorphism between time series analysis and non-parametric statistical inference

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Isomorphism between time series analysis and non-parametric statistical inference

Isomorphism between time series analysis and non-parametric statistical inference

Book Reviews

Abstract Abstract Causal Models in the Social Sciences, H.M. Blalock, Jr. (ed.). Chicago: Aldine Atherton, Inc., 1971. xi + 515 pp. $15.00 cloth, $9.75 paperback. Reviewed by Arthur S. Goldberger Statistical Issues: A Reader for the Behavioral Sciences, Roger E. Kirk (ed.). Monterey: Brooks Cole Publishing Co., 1972. x + 401 pp., $5.95 paperback. Contemporary Problems in Statistics: A Book of Readings for the Behavioral Sciences, Bernhardt Lieberman (ed.). New York: Oxford University Press Inc., 1971. xv + 446 pp. $5.50 paperback. Readings in Statistics for the Behavioral Scientist, Joseph A. Steger (ed.). New York: Holt, Rinehart, and Winston, Inc., 1971. ix + 406 pp. $5.95 paperback. Reviewed by David K. Hildebrand Dynamic Probabilistic Systems, Volume I: Markov Models and Volume II: Semi-Markov and Decision Processes, Ronald A. Howard New York: John Wiley and Sons, Inc., 1971. xvii + 576 pp., $17.95, and xviii + 531 pp., $19.95. Reviewed by John E. Rolph Linear Models, S.R. Searle New York: John Wiley and Sons, Inc., 1971. xxi + 532 pp. $19.95. Reviewed by Peter W.M. John A Short Course in Computational Probability and Statistics, W. Freiberger and U. Grenander New York: Springer-Verlag Inc., 1971. xii + 155 pp. $6.50. Reviewed by L.A. Shepp Statistics: The Essentials for Research, Henry E. Klugh New York: John Wiley and Sons, Inc., 1970. xiv+368 pp. $9.95. Reviewed by Donald L. Meyer An Introduction to Bayesian Inference in Econometrics, Arnold Zellner New York: John Wiley and Sons, Inc., 1971. xv + 431 pp. $19.95. Reviewed by Dennis Aigner Optimal Statistical Decisions, Morris H. DeGroot New York: McGraw-Hill Book Co., 1970, xvi + 489 pp. $14.50. Reviewed by David Siegmund Selected Tables in Mathematical Statistics, H. Leon Harter and D.B. Owen (eds.). Chicago: Markham Publishing Company, 1970, v + 405 pp. $5.80. Reviewed by Morty A. Yalovsky and George P.H. Styan Cash Management and the Demand for Money, Daniel Orr New York: Praeger Publishers, 1970, xii + 212 pp. $11.75. Reviewed by George F. Brown, Jr. Selected Readings in Econometrics from Econometrica, John W. Hooper and Marc Nerlove (eds.). Cambridge: The MIT Press, 1970, viii + 498 pp., $15.00. Reviewed by Robert F. Engle An Introduction to the Theory of Statistics, R.L. Plackett New York: Barnes and Noble, Inc., 1971. 204 pp. $5.50 paperback. Reviewed by David R. Brillinger Statistical Inference, S.D. Silvey New York: Penguin Books, Inc., 1970. 192 pp. $5.95 paperback. Reviewed by L.H. Koopmans Multivariate Morphometrics, R.E. Blackith and R.A. Reyment New York: Academic Press Inc., 1971, ix + 412 pp. $16.00. Reviewed by Robert R. Sokal Statistical Methods of Econometrics, E. Malinvaud Amsterdam: North Holland Publishing Co., 2nd ed., 1970. xv + 744 pp. $17.25. Reviewed by E. Lyttkens Regression and Econometric Methods, David S. Huang New York: John Wiley and Sons, 1970, xiii + 274 pp. $12.95. Reviewed by Vincent J. Geraci Nonparametric Statistical Inference, Jean Dickinson Gibbons New York: McGraw-Hill Book Co., 1970, xiv+306 pp. $11.95. Reviewed by Edward J. Dudewicz and Nancy L. Geller Probability and Mathematical Statistics: An Introduction, Eugene Lukacs New York: Academic Press Inc., 1971. x + 242 pp. $8.50. Reviewed by Michael Orkin Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume I: Theory of Statistics, Lucien M. LeCam Jerzy Neyman and Elizabeth L. Scott (eds.). Berkeley: University of California Press, 1972. xiii + 760 pp. $28.50. Elements of Finite Probability, William J. Adams New York: Kaedmon Publishing Co., 1971. xi + 194 pp. $5.95 (Study Guide $3.95). Modern Mathematical Methods for Economics and Business, Ronald E. Miller New York: Holt, Rinehart and Winston, Inc., 1971. xii + 488 pp. $13.00. The Elements of Biometry, Kenneth Mather New York: Barnes and Noble, Inc., 1972. x + 193 pp. $5.50 cloth, $3.25 paperback.

On the Asymptotic Efficiency of the Kolmogorov-Smirnov Test

Abstract The Kolmogorov-Smirnov test is important in nonparametric statistical inference. The limiting distribution of the Kolmogorov-Smirnov statistic under the null hypothesis is well known and has been derived by several different methods. The limiting distribution of this statistic under the alternative hypothesis is unknown so that it is not possible, in general, to compute the power of the Kolmogorov-Smirnov test. It is possible, however, to compute a lower bound for the power of this test. This result is used to calculate a lower bound for the asymptotic efficiency of the Kolmogorov-Smirnov test relative to the optimum likelihood ratio test. Applications are given to Cauchy, exponential and normal populations. In addition, a lower bound for the asymptotic efficiency of the Kolmogorov-Smirnov test relative to the t-test is computed for translation alternatives.

Analysis and Inference for Incompletely Specified Models Involving the Use of Preliminary Test(s) of Significance

statistical-mathematical model. (B) Problems of estimation and tests of hypotheses. These involve a choice of appropriate functions of the sample observations, called statistics, to estimate the values of, or to test hypotheses concerning, the parameters in the statistical-mathematical model. (C) Problems of distribution. These include the mathematical derivation of the distributions in random samples of the statistics used as estimators or test criteria in order that valid inferences may be made concerning the population parameters in the specified statistical-mathemnatical model. In more recent times non-parametric or distribution-free statistical inference procedures, not requiring a model specification, have been and are being considerably extended: nevertheless most applications of statistics in scientific research are still parametric in nature. This paper will be concerned with problems of specification. In discussing problems of specification Fisher [1922] was of the opinion that an appropriate statistical-mathematical model, to be used in describing an observation in an investigation, should be determined in advance by the investigator. Further, that this should be done from theoretical considerations in the particular substantive field and/or from curve fitting studies based on independent extensive uniformity type data. In this latter case the adequacy of the choice of the model may be tested a posteriori; for example, by some 'goodness of fit' test.

A Note on the Asymptotic Normality of the Mann-Whitney-Wilcoxon Statistic

Abstract The Mann-Whitney-Wilcoxon statistic is of some importance in non-parametric statistical inference. The asymptotic normality of this statistic has been established previously for the case where the distributions of the random variables, in each of the two samples, are the same. In the present work it is shown that this statistic is asymptotically normal when these distributions are not all the same. An application of this result to a particular hypothesis testing problem is also given.

A Note on the Asymptotic Normality of the Mann-Whitney-Wilcoxon Statistic

Abstract The Mann-Whitney-Wilcoxon statistic is of some importance in non-parametric statistical inference. The asymptotic normality of this statistic has been established previously for the case where the distributions of the random variables, in each of the two samples, are the same. In the present work it is shown that this statistic is asymptotically normal when these distributions are not all the same. An application of this result to a particular hypothesis testing problem is also given.