A Note on the Asymptotic Distribution of Berk—Jones Type Statistics under the Null Hypothesis

SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL

Econometric Theory ◽

10.1017/s0266466609990430 ◽

2009 ◽

Vol 26 (4) ◽

pp. 965-993 ◽

Cited By ~ 7

Author(s):

Christian Francq ◽

Lajos Horvath ◽

Jean-Michel Zakoïan

Keyword(s):

Time Series ◽

Asymptotic Distribution ◽

Null Hypothesis ◽

Nuisance Parameter ◽

Time Series Models ◽

Ratio Test ◽

Finite Sample ◽

Chi Square ◽

Finite Sample Properties ◽

Linearity Testing

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.

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A test for block circular symmetric covariance structure with divergent dimension

ESAIM Probability and Statistics ◽

10.1051/ps/2019020 ◽

2019 ◽

Vol 23 ◽

pp. 672-696

Author(s):

Junshan Xie ◽

Gaoming Sun

Keyword(s):

Numerical Simulations ◽

Sample Size ◽

Asymptotic Distribution ◽

Null Hypothesis ◽

Covariance Structure ◽

Moderate Deviation ◽

Test Method ◽

Test Statistic ◽

Lr Test ◽

Structure Test

The paper considers the likelihood ratio (LR) test on the block circular symmetric covariance structure of a multivariate Gaussian population with divergent dimension. When the sample size n, the dimension of each block p and the number of blocks u satisfy pu < n − 1 and p = p(n) → ∞ as n → ∞, the asymptotic distribution and the moderate deviation principle of the logarithmic LR test statistic under the null hypothesis are established. Some numerical simulations indicate that the proposed LR test method performs well in the divergent-dimensional block circular symmetric covariance structure test.

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Testing for Harmonic New Better than used in Expectation

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800005283 ◽

1998 ◽

Vol 12 (3) ◽

pp. 409-416 ◽

Cited By ~ 9

Author(s):

S. Rao Jammalamadaka ◽

Eun-Soo Lee

Keyword(s):

Exponential Distribution ◽

Asymptotic Distribution ◽

Relative Efficiency ◽

Null Hypothesis ◽

Asymptotic Relative Efficiency ◽

Distribution Theory ◽

Asymptotic Distribution Theory ◽

Leukemia Data ◽

New Better Than Used ◽

Better Than

A statistic for testing the null hypothesis that F is the exponential distribution against the alternative of harmonic new better than used in expectation (HNBUE) is proposed. The asymptotic distribution theory for this statistic is derived under the null hypothesis and asymptotic relative efficiency (ARE) with respect to other competing tests for HNBUE is evaluated. This test is applied to the leukemia data described in Bryson and Siddiqui (1969).

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Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

Econometric Theory ◽

10.1017/s0266466600004138 ◽

1987 ◽

Vol 3 (1) ◽

pp. 69-97 ◽

Cited By ~ 33

Author(s):

M. Hashem Pesaran

Keyword(s):

Probability Density ◽

Asymptotic Distribution ◽

Null Hypothesis ◽

Probability Density Functions ◽

Density Functions ◽

Local Alternatives ◽

Hypotheses Testing ◽

Local Power ◽

Test Statistic ◽

Local Alternative

This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

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An Alternative to Cohen's κ

European Psychologist ◽

10.1027/1016-9040.11.1.12 ◽

2006 ◽

Vol 11 (1) ◽

pp. 12-24 ◽

Cited By ~ 19

Author(s):

Alexander von Eye

Keyword(s):

Simulation Study ◽

Null Hypothesis ◽

Categorical Variables ◽

Alternative Measure ◽

Rater Agreement ◽

Verbal Processing ◽

Heavy Tailed ◽

Applicant Selection

At the level of manifest categorical variables, a large number of coefficients and models for the examination of rater agreement has been proposed and used. The most popular of these is Cohen's κ. In this article, a new coefficient, κ s , is proposed as an alternative measure of rater agreement. Both κ and κ s allow researchers to determine whether agreement in groups of two or more raters is significantly beyond chance. Stouffer's z is used to test the null hypothesis that κ s = 0. The coefficient κ s allows one, in addition to evaluating rater agreement in a fashion parallel to κ, to (1) examine subsets of cells in agreement tables, (2) examine cells that indicate disagreement, (3) consider alternative chance models, (4) take covariates into account, and (5) compare independent samples. Results from a simulation study are reported, which suggest that (a) the four measures of rater agreement, Cohen's κ, Brennan and Prediger's κ n , raw agreement, and κ s are sensitive to the same data characteristics when evaluating rater agreement and (b) both the z-statistic for Cohen's κ and Stouffer's z for κ s are unimodally and symmetrically distributed, but slightly heavy-tailed. Examples use data from verbal processing and applicant selection.

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