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Article

Keywords:
continuity of invariant statistics; translation invariant statistic; scale invariant statistics; joint distribution; marginal distribution
Summary:
The aim of this paper is to establish theorems on the absolute continuity of translation as well as scale invariant statistics in general, from which the related results by Hodges-Lehmann and Puri-Sen follow. The continuity relations between the joint cdf of a random vector and its marginal cdf's are also considered.
References:
[1] P. J. Bickel E. L. Lehmann: Descriptive statistics for nonparametric models. I. Introduction. Ann. Statist. (1975), V. 3, N. 5, 1038-1044. DOI 10.1214/aos/1176343239 | MR 0395020
[2] P. J. Bickel E. L. Lehmann: Descriptive statistics for nonparametric models. II. Location. Ann. Statist. (1975), V. 3, N. 5, 1045-1069. MR 0395021
[3] J. L. Hodges, Jr. E. L. Lehmann: Estimates of location based on rank tests. Ann. Math. Stat. (1963), V. 34, 598-611. DOI 10.1214/aoms/1177704172 | MR 0152070
[4] M. L. Puri P. K. Sen: Nonparametric methods in multivariate analysis. New York, 1971. MR 0298844
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