Adaptive estimation of the conditional cumulative distribution function from current status data

作者：Plancade Sandra^*

来源：Journal of Statistical Planning and Inference, 2013, 143(9): 1466-1485.

DOI：10.1016/j.jspi.2013.04.005

• Current status
• Interval censoring
• Distribution function
• Model selection
• Adaptivity
• Anisotropic Besov spaces
• Minimax

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:delta = I((Y <= T)) with 0 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,delta). <br xmlns:set="http://exslt.org/sets">A collection of finite-dimensional linear subsets of L-2(R-2) called models are built as tensor products of classical approximation spaces of L-2(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.

• 出版日期2013-9