New efficient spline estimation for varying-coefficient models with two-step knot number selection

One of the advantages for the varying-coefficient model is to allow the coefficients to vary as smooth functions of other variables and the coefficients functions can be estimated easily through a simple B-spline approximations method. This leads to a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when some coefficient functions possess different degrees of smoothness. Under the regularity conditions, the consistency and asymptotic normality of the two step B-spline estimators are also derived. A few simulation studies show that the gain by the two-step procedure can be quite substantial. The methodology is illustrated by an AIDS data set.