Adaptive warped kernel estimators

International audienceIn 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 $(\Phi(X),Y)$, with $\Phi$ a one-to-one function, to build a collection 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 additive 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-off 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