학술논문

On some two-step density estimation method.
Document Type
Journal
Author
Jarnicka, Jolanta AMS Author Profile
Source
Universitatis Iagellonicae. Acta Mathematica (Univ. Iagel. Acta Math.) (20050101), No. 43, 67-91. ISSN: 0083-4386 (print).eISSN: 2084-3828.
Subject
62 Statistics -- 62G Nonparametric inference
  62G07 Density estimation
Language
English
Abstract
This paper presents an original method for estimating a density. Theestimator is mixture of kernel estimators of components of an``approximate normal mixture model'' for the data. The formula of theAsymptotic Mean Integrated Square Error is established. A simulationis conducted to assess the performance of the method.\parAlthough the simulation carried out in the paper suggests that the newmethod might be superior under certain circumstances, the method needsfurther studies to be considered as a sound alternative to classicalapproaches. The consistency properties are proven when the parametersof the mixing model are nonrandom. However, in practice (as in thesimulation), they are to be estimated. Also, the selection of thenumber of mixture components is yet to be addressed.

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