Article ID Journal Published Year Pages File Type
1147832 Journal of Statistical Planning and Inference 2013 20 Pages PDF
Abstract

•We propose an adaptive estimator for conditional cumulative distribution function from current status data.•The estimator is built by minimization of a least-square contrast followed by a model selection procedure.•Minimax rates over anisotropic balls are computed.•A numerical study emphasizes the impact of the distance between the observation and survival time distribution.

Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T  : δ=I{Y≤T}δ=I{Y≤T} with II the indicator function. This paper presents a procedure to estimate the conditional cumulative distribution function F of Y given X   from an independent identically distributed sample of (X,T,δ)(X,T,δ).A collection of finite-dimensional linear subsets of L2(R2)L2(R2) called models are built as tensor products of classical approximation spaces of L2(R)L2(R). Then a collection of estimators of F is constructed by minimization of a regression-type contrast on each model and a data driven procedure allows to choose an estimator among the collection. We show that the selected estimator converges as fast as the best estimator in the collection up to a multiplicative constant and is minimax over anisotropic Besov balls. Finally simulation results illustrate the performance of the estimation and underline parameters that impact the estimation accuracy.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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