Splines in statistics. (English) Zbl 0534.62017

Wegman, Edward J.; Wright, Ian W.

J. Am. Stat. Assoc. 78, 351-365 (1983).

The paper provides a survey of work on splines in statistics. Splines are presented as a nonparametric function estimating technique. General introduction to the theory of interpolating and smoothing splines is given and the following topics are discussed:
Splines in the nonparametric regression setting; the method of cross- validation for choosing the smoothing parameter; splines and the general multivariate regression (surface) estimation; splines as nonparametric density estimators; splines in time series analysis; splines in statistical inference under order restrictions (isotonic regression). A number of open problems relating to splines in statistics is mentioned. The reference list contains more than 120 titles dated up to 1983. It is to be noted that the name Derek G. is to be read Derek G. Hudson.

Reviewer: G.Ya.Seliger

MSC:

62G05	Nonparametric estimation
65D07	Numerical computation using splines

Keywords:

interpolation; functional estimation; bibliography; survey; smoothing splines; cross-validation; density estimators; time series; order restrictions; isotonic regression