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On the optimal number of classes in the Pearson goodness-of-fit tests

Domingo Morales, Leandro Pardo, Igor Vajda (2005)

Kybernetika

An asymptotic local power of Pearson chi-squared tests is considered, based on convex mixtures of the null densities with fixed alternative densities when the mixtures tend to the null densities for sample sizes n → ∞ . This local power is used to compare the tests with fixed partitions 𝒫 of the observation space of small partition sizes | 𝒫 | with the tests whose partitions 𝒫 = 𝒫 n depend on n and the partition sizes | 𝒫 n | tend to infinity for n → ∞ . New conditions are presented under which it is asymptotically optimal...

On the role played by the fixed bandwidth in the Bickel-Rosenblatt goodness-of-fit test.

Carlos Tenreiro (2005)

SORT

For the Bickel-Rosenblatt goodness-of-fit test with fixed bandwidth studied by Fan (1998) we derive its Bahadur exact slopes in a neighbourhood of a simple hypothesis f = f0 and we use them to get a better understanding on the role played by the smoothing parameter in the detection of departures from the null hypothesis. When f0 is an univariate normal distribution and we take for kernel the standard normal density function, we compute these slopes for a set of Edgeworth alternatives which give...

On two tests based on disjoint m-spacings

Franciszek Czekała (1998)

Applicationes Mathematicae

This paper is concerned with the properties of two statistics based on the logarithms of disjoint m-spacings. The asymptotic normality is established in an elementary way and exact and asymptotic means and variances are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1]. Bahadur approximate efficiency of tests based on those statistics is found for such alternatives....

Optimal nonlinear transformations of random variables

Aldo Goia, Ernesto Salinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....

Permutation tests for multiple changes

Marie Hušková, Aleš Slabý (2001)

Kybernetika

Approximations to the critical values for tests for multiple changes in location models are obtained through permutation tests principle. Theoretical results say that the approximations based on the limit distribution and the permutation distribution of the test statistics behave in the same way in the limit. However, the results of simulation study show that the permutation tests behave considerably better than the corresponding tests based on the asymptotic critical value.

Power of A Class of Goodness-of-Fit Tests I

Christopher S. Withers, Saralees Nadarajah (2009)

ESAIM: Probability and Statistics

Consider testing whether F = F0 for a continuous cdf on R = (-∞,∞) and for a random sample X1,..., Xn from F. We derive expansions of the associated asymptotic power based on the Cramer-von Mises, Kolmogorov-Smirnov and Kuiper statistics. We provide numerical illustrations using a double-exponential example with a shifted alternative.

Randomized goodness of fit tests

Friedrich Liese, Bing Liu (2011)

Kybernetika

Classical goodness of fit tests are no longer asymptotically distributional free if parameters are estimated. For a parametric model and the maximum likelihood estimator the empirical processes with estimated parameters is asymptotically transformed into a time transformed Brownian bridge by adding an independent Gaussian process that is suitably constructed. This randomization makes the classical tests distributional free. The power under local alternatives is investigated. Computer simulations...

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