A note on the best invariant estimation of continuous probability distributions under mean square loss
Data Analysis, Statistics and Probability
2017-08-29 v2 Statistics Theory
Statistics Theory
Abstract
We consider the nonparametric estimation problem of continuous probability distribution functions. For the integrated mean square error we provide the statistic corresponding to the best invariant estimator proposed by Aggarwal (1955) and Ferguson (1967). The table of critical values is computed and a numerical power comparison of the statistic with the traditional Cram\'{e}r-von Mises statistic is done for several representative distributions.
Keywords
Cite
@article{arxiv.1510.06419,
title = {A note on the best invariant estimation of continuous probability distributions under mean square loss},
author = {Thomas Schürmann},
journal= {arXiv preprint arXiv:1510.06419},
year = {2017}
}
Comments
5 pages, 1 table, 2 figures, (typo corrected)