Consistent Residuals Density Estimation in Nonparametric Regression Under m(n)-Dependent Sample

Abstract:

      Consider the nonparametric regression model Y_i=M(X_i)+e_i，where M(x) is an unknown real function on B(?R), {(X_i,Y_i)} is a m(n)-dependent sample from (X,Y), the residuals{e_i}have unknown common density f(x).In this paper, a non-parametric estimate for f(x)is proposed on the basis of the residuals estimates. The estimate is shown to be pointwise and uniformly consistent and L₁-consistent.