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arXiv · 1809.02691

The smoothness test for a density function

Bogdan Ćmiel·Karol Dziedziul·Barbara Wolnik
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Abstract

The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ 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.

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Bogdan Ćmiel, Karol Dziedziul, Barbara Wolnik. 2018-09-07. The smoothness test for a density function. https://doi.org/10.1016/j.na.2014.03.004

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