arXiv subjects

Leigh A Roberts

Publications and source records attributed to Leigh A Roberts.

3 recordsLinked to original sources

arXiv2025

A note on goodness of fit testing for the Poisson distribution

Since its introduction in 1950, Fisher's dispersion test has become a standard means of deciding whether or not count data follow the Poisson distribution. The test is based on a characteristic property of the Poisson distribution, and discriminates well between the Poisson and the natural alternative hypotheses of binomial and negative binomial distributions. While the test is commonly used to test for general deviations from Poissonity, its performance against more general alternatives has not been widely investigated. This paper presents realistic alternative hypotheses for which general goodness of fit tests perform much better than the Fisher dispersion test.

stat.AP↗

arXiv2021

On the derivation of the Khmaladze transforms

Some 40 years ago Khmaladze introduced a transform which greatly facilitated the distribution free goodness of fit testing of statistical hypotheses. In the last decade, he has published a related transform, broadly offering an alternative means to the same end. The aim of this paper is to derive these transforms using relatively elementary means, making some simplifications, but losing little in the way of generality. In this way it is hoped to make these transforms more accessible and more widely used in statistical practice. We also propose a change of name of the second transform to the Khmaladze rotation, in order to better reflect its nature.

math.ST↗

arXiv2018

Distribution free testing of grouped Bernoulli trials

Recently Khmaladze has shown how to `rotate' one empirical process to another. This paper is the first to apply this transform when successive data points are generated by a single distributional family, but with covariates varying over the sample. The application is to Bernoulli trials, and new results show how group sizes rotated are related to the number of parameters, and explore the impact of different types of data generating processes. The utility of the rotation is clear: goodness of fit tests after rotation to a distribution free process are easily computed, show excellent convergence properties, and exhibit high power to reject incorrect null hypotheses.

stat.AP↗