Density smoothness estimation problem using a wavelet approach. (28th November 2013)

• Record Type: Journal Article
• Authors: Dziedziul, Karol; Ćmiel, Bogdan
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 130
• Page End: 144
• Publication Date: 2013-11-28
• Subjects: Estimation, -- wavelets, -- Besov spaces, -- smoothness parameter; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2013030
• Languages: English
• ISSNs: 1292-8100

Abstract

Abstract : In this paper we consider a smoothness parameter estimation problem for a density function. The smoothness parameter of a function is defined in terms of Besov spaces. This paper is an extension of recent results (K. Dziedziul, M. Kucharska, B. Wolnik, Estimation of the smoothness parameter ). The construction of the estimator is based on wavelets coefficients. Although we believe that the effective estimation of the smoothness parameter is impossible in general case, we can show that it becomes possible for some classes of the density functions.