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Editor: Universidad Carlos III de Madrid. Departamento de Estadística

Issued date: 1996-03

Serie-No.: UC3M Working papers. Statistics and Econometrics96-30

Keywords: Continuous mixtures , Cross-validation , Fission track analysis , Kernel density estimation

Rights: Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:We present a method to estimate the latent distribution for a mixture model. Our method is motivated by the standard kernel density estimation but instead of using an estimate based on the unobserved latent variables, we take the expectation with respect to thWe present a method to estimate the latent distribution for a mixture model. Our method is motivated by the standard kernel density estimation but instead of using an estimate based on the unobserved latent variables, we take the expectation with respect to their distribution conditional on the data. The resulting estimator is continuous and, hence, is appropriate when there is a strong belief in the continuity of the mixing distribution. We present an asymptotic justification and we discuss the associated computational problems. The method is illustrated by an example of fission track analysis where we estimate the densi ty of the age of crystals.+-





Autor: Goutis, Constantinos

Fuente: http://e-archivo.uc3m.es


Introducción



Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Estadística DES - Working Papers.
Statistics and Econometrics.
WS 1996-03 Nonparametric estimation of a mixing density via the kernel method Goutis, Constantinos http:--hdl.handle.net-10016-10437 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid NONPARAMETRIC ESTIMATION OF A MIXING DENSITY VIA THE KERNEL METHOD Constantinos Goutis 96-30 C-) ~ LU 0. « 0. Universidad Carlos III de Madrid Working Paper 96-30 Statistics and Econometrics Series 09 May 1996 Departamento de Estadfstica y Econometrfa Universidad Carlos III de Madrid Calle Madrid 126 28903 Getafe (Spain) Fax (341) 624-9849 NONPARAMETRIC ESTIMATION OF A MIXING DENSITY VIA THE KERNEL METHOD Constantinos Goutis* Abstract ______________________________________________________________ vVe present a method to estimate the latent distribution for a mixture model.
Our method is motivated by the standard kernel density estimation but instead of using an estimate based on the unobserved latent variables, we take the expectation with respect to their distribution conditional on the data.
The resulting estimator is continuous and, hence, is appropriate when there is a strong belief in the continuity of the mixing distribution.
We present an asymptotic justification and we discuss the associated computational problems. The method is illustrated by an example of fission track analysis where we estimate the densi ty of the age of crystals. Key words and phrases: Continuous mixtures, cross-validation, fission track analysis, kernel density estimation. * Departamento de Estadfstica y Econometrfa, Universidad Carlos III de Madrid, tel. (341) 624-9852, e-mail: costas@est-econ.uc3m.es.
The research was partially carried out during a visit in and supported by CREST-Paris France.
I would like to thank Christian Robert for his hospitality and useful discus...





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