ADAPTIVE WARPED KERNEL ESTIMATORS GAËLLE CHAGNY

Abstract. In this work, we develop a method of adaptive nonparametric estimation, based on "warped " kernels. The aim is to estimate a real-valued function s from a sample of random couples (X;Y). We deal with transformed data ((X); Y), with a one-to-one function, to build a collec-tion of kernel estimators. The data-driven bandwidth selection is done with a method inspired by Goldenshluger and Lepski (2011). The method permits to handle various problems such as addi-tive and multiplicative regression, conditional density estimation, hazard rate estimation based on randomly right censored data, and cumulative distribution function estimation from current-status data. The interest is threefold. First, the squared-bias/variance trade-o is automatically realized. Next, non-asymptotic risk bounds are derived. Last, the estimator is easily computed thanks to its simple expression: a short simulation study is presented