Ansley, Craig F.; Kohn, Robert; Wong, Chi-Ming Nonparametric spline regression with prior information. (English) Zbl 0771.62027 Biometrika 80, No. 1, 75-88 (1993). 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 \(O(n)\) algorithms to compute the estimate of the regression curve and the cross-validation and maximum likelihood criterion functions. Cited in 16 Documents MSC: 62G07 Density estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 65D07 Numerical computation using splines 65D10 Numerical smoothing, curve fitting Keywords:Bayesian confidence interval; filtering; periodic spline; spline smoothing; state space model; prior information; nonparametric regression; family of parametric curves; linear differential equation; penalized least squares; smoothness penalty; growth and decay curves; time transformation; linear equality constraints; generalized cross- validation; maximum likelihood; efficient \(O(n)\) algorithms PDFBibTeX XMLCite \textit{C. F. Ansley} et al., Biometrika 80, No. 1, 75--88 (1993; Zbl 0771.62027) Full Text: DOI