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Data driven efficient score tests for Poissonity

Inglot Tadeusz

Probability and Mathematical Statistics

2019

Vol. 39, Fasc. 1

115--126

New data driven score tests for testing goodness of fit of the Poisson distribution are proposed. They are direct applications of the general construction of data driven goodness-of-fit tests for composite hypotheses developed in Inglot et al. (1997). By a simulation study it is shown that these tests perform almost equally well as the best known solutions for standard alternatives and outperform them for more difficult alternatives.

Refined data driven tests for univariate symmetry

Inglot T., Kujawa D.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 1

91--106

We propose a modification of the data driven score rank tests studied recently in Inglot et al. (2012) by an appropriate choice of the orthonormal system. The simulation study confirms much better performance of the new tests for alternatives with dominating asymmetry in the tails and comparable sensitivity for other types of alternatives. In effect we obtain omnibus tests for symmetry which are equal to the best existing procedures for typical alternatives and overtake them significantly for atypical ones.

Data driven tests for univariate symmetry about an unknown median

Inglot T., Janic A.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 2

317--336

We propose new data driven score rank tests for univariate symmetry about an unknown center. We construct test statistics, state assumptions and define estimators of nuisance parameters. We prove that the test statistics are asymptotically distribution-free under the null hypothesis. Using simulations, we verify these asymptotic results for finite samples and show that, under the assumptions and when they are somewhat violated, the size of the test is stable when changing the null distribution. We also compare the empirical behaviour of the new tests with those proposed in the literature. We show that for families of distributions commonly applied to model asymmetry the new tests overcome their competitors on average and for most individual alternatives.

Data driven tests for univariate symmetry

Inglot T., Janic A., Józefczyk J.

Probability and Mathematical Statistics

2012

Vol. 32, Fasc. 2

323--358

We propose new data driven score rank tests for univariate symmetry around a known center.We apply both Schwarz-type and recently introduced data driven penalty selection rules. Some key asymptotic results regarding the test statistics are given and some asymptotic optimality properties proved. In an extensive simulation study, we compare the empirical behaviour of these tests to tests found in the recent literature to be powerful. We show that, for a broad range of asymmetric distributions, data driven tests have stable power, which is comparable to their competitors for typical alternatives and much greater for some atypical alternatives.

Data driven score tests for univariate symmetry based on non-smooth functions

Józefczyk J.

Probability and Mathematical Statistics

2012

Vol. 32, Fasc. 2

301--322

We propose data driven score rank tests for univariate symmetry around a known center based on non-smooth functions. A choice of non-smooth functions is motivated by very special properties of a certain function on [0; 1] determined by a distribution which is responsible for its asymmetry. We modify recently introduced data driven penalty selection rules and apply Schwarz-type penalty as well. We prove basic asymptotic results for the test statistics. In a simulation study we compare the empirical behavior of the new tests with the data driven tests based on the Legendre basis and with the so-called hybrid test. We show good power behavior of the new tests often overcoming their competitors.