Summary: Let \(X\) be a random vector taking values in \(\mathbb{R}^ d\) and let \(Y\) be a non-negative bounded random variable. Moreover, assume a right censoring random variable \(C\), with continuous distribution function, operating on \(Y\), independently of \(X\) and \(Y\). In this randomly censored situation, we want to estimate \(Y\) based on the vector \(X\) of covariates, so that the mean squared error is minimized.
For this purpose we construct a nonparametric partitioning estimate \(m_ n(x)\), which is a histogram-like mean regression function estimate, and prove its strong consistency under no smoothness condition on the regression function or on the distribution of \(X\), in the sense that the integrated squared error between the estimate and the regression function tends to zero almost surely as the sample size \(n\) tends to infinity.