The paper establishes the conditions under which the generalised least squares estimator of the regression parameters is equivalent to the weighted least squares estimator. The equivalence conditions have interesting applications in local polynomial regression and kernel smoothing. Specifically,...

In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous alternatives, and are also illustrated through...