Optimal Choice of Splines and Knots in TPSPLINE and TRANSREG Procedures

Multivariate functions observed with noise can be approximated by thin-plate smoothing splines. It does not depend on the assumptions of the parametric model. The amount of smoothing can be judged by generalized cross validation. If there is no prior knowledge about the model and the data is unable to represent a model with fixed number of parameters then TPSPLINE procedure is appropriate. With the increase in sample size, the model space also increases but this situation can be handled by thin-plate smoothing spline i.e. it is suitable for complicated situations. We worked on optimal choice of knots in TPSPLINE procedure. The procedure has been demonstrated by taking real life data set. The TRANSREG procedure which is applicable to many models including ordinary, multiple, multivariate regression with variable transformations is also discussed. It can also fit regression functions with smooth, spline or penalized B-splines. This procedure uses the method of alternating least-squares, that is, finding least-square estimates of the model parameters given the current scoring of the data, and then finding least-square estimates of the scoring parameters based on the current set of model parameters. In this paper, the fitting of the model through penalized B-splines using splines for AICC, AIC, CV, SBC and GCV criterion have been discussed and compared by taking a real life data set.