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Monday, October 5, 2020 | History

11 edition of Asymptotic efficiency of nonparametric tests found in the catalog.

Asymptotic efficiency of nonparametric tests

by Nikitin, IНЎA. IНЎU.

  • 72 Want to read
  • 6 Currently reading

Published by Cambridge University Press in Cambridge, New York .
Written in English

    Subjects:
  • Nonparametric statistics,
  • Asymptotic efficiencies (Statistics)

  • Edition Notes

    Includes bibliographical references (p. 249-264) and index.

    StatementYakov Nikitin.
    Classifications
    LC ClassificationsQA278.8 .N55 1995
    The Physical Object
    Paginationxvi, 274 p. ;
    Number of Pages274
    ID Numbers
    Open LibraryOL1084972M
    ISBN 100521470293, 0521470293
    LC Control Number94008820

    An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman Pearson and LeCam’s theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models. Constancy of distributions: asymptotic efficiency of certain nonparametric tests of constancy.

    An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models. Efficiency (statistics) In the comparison of various statistical procedures, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator, experiment, or test needs fewer observations than a less efficient one to achieve a given performance.

    Book Description. Proven Material for a Course on the Introduction to the Theory and/or on the Applications of Classical Nonparametric Methods. Since its first publication in , Nonparametric Statistical Inference has been widely regarded as the source for learning about nonparametric statistics. The fifth edition carries on this tradition while thoroughly revising at least 50 percent of. However, one must consider the cost, in terms of power, of applying the nonparametric test when indeed the data are distributed normally and satisfy the other assumptions of the parametric test. With this comes the notion of Asymptotic Relative Efficiency (ARE).Cited by:


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Asymptotic efficiency of nonparametric tests by Nikitin, IНЎA. IНЎU. Download PDF EPUB FB2

Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests.

An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman-Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models Cited by: 1.

Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where there exist numerous heuristic tests such as the Kolmogorov-Smirnov, Cramer-von Mises, and linear rank tests.

Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. Asymptotic efficiency of nonparametric goodness-of-fit tests; 3. Asymptotic efficiency of nonparametric homogeneity tests; 4.

Asymptotic efficiency of nonparametric symmetry tests; 5. Asymptotic efficiency of nonparametric independence tests; 6. Local asymptotic optimality of nonparametric tests and the characterisation of distributions.

Introduction to the Theory of Nonparametric Statistics U-statistics, asymptotic efficiency, the Hodges-Lehmann technique for creating a confidence interval and a point estimator from a test, linear rank statistics, and more. Also includes currently developing areas.

Readers are required to be familiar with the basic concepts of statistical Cited by: Chapter 6 Nonparametric tests. This chapter overviews some of the most well-known nonparametric tests are intended for a variety of purposes, but mostly related to: (i) the evaluation of the goodness-of-fit of a distribution model to a dataset; (ii) the assessment of the relation between two random variables.A nonparametric test evaluates a null hypothesis \(H_0\) against an.

Nonparametric tests, on the other hand, do not require any strict distributional assumptions. Even if the data are distributed normally, nonparametric methods are often almost as powerful as parametric methods. Many nonparametric methods analyze the ranks of.

2 Lecture Asymptotic Relative Efficiency Definition 2 (Asymptotic relative efficiency). The Asymptotic Relative Efficiency (ARE) is the ratio of the squares of slopes between two statistics.

Example 3 (Sign test). This example is from Van der Vaart, but presents a different derivation than is found in the Size: 75KB. Alternative Efficiencies for Signed Rank Tests Klotz, Jerome, Annals of Mathematical Statistics, ; Asymptotic Efficiency of a Class of Non-Parametric Tests for Regression Parameters Adichie, J.

N., Annals of Mathematical Statistics, ; Local Asymptotic Power of Quadratic Rank Tests for Trend Beran, Rudolf, Annals of Statistics, Cited by: It is well-known that the asymptotic relative efficiency (ARE) of the Wilcoxon signed rank test is 3 π ≈ compared to Student's t -test, if the data are drawn from a normally distributed population.

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the 5/5(2).

If a test is based on a statistic which has asymptotic distribution different from normal or chi-square, a simple determination of the asymptotic efficiency is not possible. We may define the asymptotic efficiency e along the lines of Remark and Remark. ASYMPTOTIC DISTRIBUTION THEORY FOR NONPARAMETRIC ENTROPY MEASURES OF SERIAL DEPENDENCE BY YONGMIAO HONG AND HALBERT WHITE1 Entropy is a classical statistical concept with appealing properties.

Establishing as- ymptotic distribution theory for smoothed nonparametric entropy measures of depen- dence has so far proved Size: 5MB. Abstract. Asymptotic normality of linear rank statistics for testing the hypothesis of independence is established under fixed alternatives.

A generalization of a result of Bhuchongkul [I) is obtained both with respect to the conditions concerning the orders of magnitude of the score functions and with respect to the smoothness conditions on these by: nonparametric tests in competition with t and F tests, which are known to be The asymptotic efficiency of the median test for location for normal populations is therefore (12) 1 (mn 2 1 (d{h2 = 2 mn/4(m + n) y2rj(m +n)/ 1/m +1 /nVd 7r the same as given by Cochran [3] for the sign test.

Rank test. The asymptotic theory of tests in parametric and nonparametric models and their relative efficiency is presented here.

In particular, livelihood ratio, Wald’s test and chisquare tests are derived in parametric models. The nonparametric tests discussed include two-sample rank tests and the Kolmogorov–Smirnov : Rabi Bhattacharya, Lizhen Lin, Victor Patrangenaru. Fundamentals of Nonparametric Bayesian Inference is the first book to comprehensively cover models, methods, and theories of Bayesian nonparametrics.

Readers can learn basic ideas and intuitions as well as rigorous treatments of underlying theories and computations from this wonderful book.'Cited by: The computation of certain asymptotic efficiencies for given two-sample tests against normal alternatives to the null hypothesis.

Published in The Annals of Mathematical Statistics, Sept. ) This report is part of the RAND Corporation paper series. The presented monograph is devoted to the analysis and calculation of the asymptotic efficiency of nonparametric tests.

The asymptotic efficiency is a fundamental notion of statistics. On the Asymptotic Efficiency of Normality Tests Based and calculation of the asymptotic efficiency of nonparametric tests.

The asymptotic efficiency is a fundamental notion of statistics.I have seen in published literature (and posted on here) that the asymptotic relative efficiency of the Wilcoxon signed rank test is at least when compared to the t test.

I have also heard that this only applies to large samples, although some books don't mentioning this (what's with that?).The ratio ψ 2 /ψ *2 = e is called the relative efficiency of the nonparametric test, since the nonparametric test based on the sample of size N is nearly equal (in terms of power) to the best test based on a sample of size eN.

For the two-sample problem the most common model is that of shift parameter, that is.