Error covariance matrix correction based approach to functional coefficient regression models with generated covariates

In this paper, we are concerned with the estimating problem of functional coefficient regression models with generated covariates. A new local polynomial estimation is proposed, which is based on error covariance matrix correction. It is shown that the resulting estimators are consistent, asymptotically normal and avoid the problem of undersmoothing. We estimate the error covariance matrix by difference based method. Therefore, the proposed new estimation avoids calibrating the covariate nonparametrically. Our difference based error covariance matrix estimator allows the order of difference to tend to be infinite and is asymptotically equivalent to the residual based estimator. In addition, we construct the simultaneous confidence bands for the underlying coefficient functions. The finite sample performance of our procedure is investigated in a simulation study and a real data set is analyzed to illustrate the usefulness of our procedure as well.