Nonparametric spline regression with prior information

SUMMARY By using prior information about the regression curve we propose new nonparametric regression estimates. We incorporate two types of information. First, we suppose that the regression curve is similar in shape to a family of parametric curves characterized as the solution to a linear differential equation. The regression curve is estimated by penalized least squares with the differential operator defining the smoothness penalty. We discuss in particular growth and decay curves and take a time transformation to obtain a tractable solution. The second type of prior information is linear equality constraints. We estimate unknown parameters by generalized cross-validation or maximum likelihood and obtain efficient 0(n) algorithms to compute the estimate of the regression curve and the cross-validation and maximum likelihood criterion functions.