The smoothness test for a density function
Statistics Theory
2018-09-11 v1 Statistics Theory
Abstract
The problem of testing hypothesis that a density function has no more than derivatives versus it has more than derivatives is considered. For a solution, the norms of wavelet orthogonal projections on some orthogonal "differences" of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution, a new technique of enrichment procedure is proposed. The finite sample behaviour of the smoothness test is demonstrated in a numerical experiment in case of determination if a density function is continues or discontinues.
Cite
@article{arxiv.1809.02691,
title = {The smoothness test for a density function},
author = {Bogdan Ćmiel and Karol Dziedziul and Barbara Wolnik},
journal= {arXiv preprint arXiv:1809.02691},
year = {2018}
}