Non-parametric probability density function estimation on a bounded support: applications to shape classification and speech coding

Samir Saoudi (1) , Faouzi Ghorbel , Alain Hillion

1 SC - Département Signal et Communications

In statistics, it is usually difficult to estimate the probability density function from N independent samples X1,X2, , XN identically distributed. A lot of work has been done in the statistical literature on the problem of probability density estimation (e.g. Cencov, 1962; Devroye and Gyorfi, 1981; Hall, 1980 and 1982; Hominal, 1979; Izenman, 1991; Kronmal and Tarter, 1968; Parzen, 1962; Rosenblatt, 1956). In this paper, we consider random variables on bounded support. Orthogonal series estimators, studied in detail by Kronmal and Tarter (1968), by Hall (1982) and by Cencov (1962), show that there is a disadvantage related to the Gibbs phenomenon on the bias of these estimators. We suggest a new method for the non-parametric probability density function estimation based on the kernel method using an appropriately chosen regular change of variable. The new method can be used for several problems of signal processing applications (scalar or vector quantization, speech or image processing, pattern recognition, etc.). Applications to shape classification and speech coding are given.

Mots clés: Kernel estimator; Bounded support; Diffeomorphism; Shape classification; Speech coding Quantization

Domaines: Traitement du signal et de l'image [eess.SP]

Samir Saoudi, Faouzi Ghorbel, Alain Hillion. Non-parametric probability density function estimation on a bounded support: applications to shape classification and speech coding. Applied Stochastic Models and Data Analysis, 1994, 10 (3), pp.215 - 231. ⟨10.1002/asm.3150100306⟩. ⟨hal-01864846⟩