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Adaptive estimation of the conditional density in presence of censoring. (English) Zbl 1193.62055
Summary: Consider an i.i.d. sample \((X_i,Y_i), i=1, \dots, n\), of observations and denote by \(\pi(x,y)\) the conditional density of \(Y_i\) given \(X_i=x\). We provide an adaptive nonparametric strategy to estimate \(\pi\). We prove that our estimator achieves optimal rates of convergence in a context of anisotropic function classes. We prove that our procedure can be adapted to positive censored random variables \(Y_i\)’s, i.e., when only \(Z_i=\inf(Y_i, C_i)\) and \(\delta_i=\mathbb1_{\{Y_i\leq C_i\}}\) are observed, for an i.i.d. censoring sequence \((C_i)_{1\leq i\leq n}\) independent of \((X_i,Y_i)_{1\leq i\leq n}\). Simulation experiments illustrate the method.

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62N01 Censored data models
65C60 Computational problems in statistics (MSC2010)
censored data