Abstract:

The paper considers the problem of nonparametric regression, which consists in estimating the derivative of the regression function, when the values of the regression function are observed with an accuracy of random errors in some known set of fixed or random points (regressors). The solution of this problem, including methods of kernel smoothing, is devoted to an extensive literature. In the paper, the consistency of a new class of locally linear estimators is studied, while a more general condition on the regressors is used. With respect to the regressors, it is only required that they asymptotically densely fill the domain of the regression function. This condition includes both the case of fixed regressors, without the requirement of regularity, and the situation of random regressors, but without the assumption of some form of weak dependence of quantities or the fulfillment of ergodic properties.