Abstract

In the paper,the varying-coefficient regression models with different smoothing variables in different coefficient functions are discussed.First,the integrated estimates of the coefficient functions are given by integrating the sample on the initial value obtained by local linear technique.Then,the improvement estimates of the coefficient functions are proposed by a one-step back-fitting procedure on the integrated estimates.The improvement estimators share the same asymptotic normalities as the local linear estimators for the varying coefficient models with a single smoothing variable in different functions.Finally the simulation example shows that the procedure is effective.

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