The smoothness test for a density function
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The problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ 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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