Estimating the integral of a squared regression function with Latin hypercube sampling

This article is concerned with the estimation of the integral of a squared regression function using Latin hypercube sampling. A class of generalized nearest-neighbour estimators is proposed and their properties are investigated with respect to various smoothness classes of regression functions. In particular, mild conditions are established which ensure that achieves a root-n convergence rate. It is further shown that has an asymptotic mean squared error smaller than that of any regular estimator based on an i.i.d. sample of the same size.