Splines in Statistics

This is a survey article that attempts to synthesize a broad variety of work on splines in statistics. Splines are presented as a nonparametric function estimating technique. After a general introduction to the theory of interpolating and smoothing splines, splines are treated in the nonparametric regression setting. The method of cross-validation for choosing the smoothing parameter is discussed and the general multivariate regression/surface estimation problem is addressed. An extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis. A comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator. The closing section provides a brief overall summary and formulates a number of open/unsolved problems relating to splines in statistics.