Publicação
Multiplicative Censoring: Estimation of a Density and its Derivatives under the Lp-Risk
| Resumo: | We consider the problem of estimating a density and its derivatives for a sample of multiplicatively censored random variables. The purpose of this paper is to present an approach to this problem based on wavelets methods. Two different estimators are developed: a linear based on projections and a nonlinear using a term-by-term selection of the estimated wavelet coefficients. We explore their performances under the Lp-risk with p ≥ 1 and over a wide class of functions: the Besov balls. Fast rates of convergence are obtained. Finite sample properties of the estimation procedure are studied on a simulated data example. |
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| Autores principais: | Abbaszadeh , Mohammad |
| Outros Autores: | Chesneau , Christophe; Doosti , Hassan |
| Assunto: | density estimation multiplicative censoring inverse problem wavelets Besov balls Lp-risk |
| Ano: | 2013 |
| País: | portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | unknown |
| Instituição associada: | Instituto Nacional de Estatística |
| Idioma: | inglês |
| Origem: | REVSTAT-Statistical Journal |
| Resumo: | We consider the problem of estimating a density and its derivatives for a sample of multiplicatively censored random variables. The purpose of this paper is to present an approach to this problem based on wavelets methods. Two different estimators are developed: a linear based on projections and a nonlinear using a term-by-term selection of the estimated wavelet coefficients. We explore their performances under the Lp-risk with p ≥ 1 and over a wide class of functions: the Besov balls. Fast rates of convergence are obtained. Finite sample properties of the estimation procedure are studied on a simulated data example. |
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