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Abstract
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 L2 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 behavior of the smoothness test is demonstrated in a numerical experiment in case of determination if a density function is continuous or discontinuous.
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Authors (3)
-
Bogdan Ćmiel
- AGH University of Science and Technology Faculty of Applied Mathematics
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.na.2014.03.004
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
no. 104,
pages 21 - 39,
ISSN: 0362-546X - Language:
- English
- Publication year:
- 2014
- Bibliographic description:
- Ćmiel B., Dziedziul K., Wolnik B.: The smoothness test for a density function// NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. -Vol. 104, (2014), s.21-39
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.na.2014.03.004
- Verified by:
- Gdańsk University of Technology
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