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statisticalplanning Journal of Statistical Planning and and inference

Summary: journal of
Journal of Statistical Planning and and inference
ELSEVIER Inference49 (1996)327 341
Improved inference in nonparametric regression using
Lk-Smoothing splines
Felix Abramovich l, David M. Steinberg*
Department of Statistics and Operations Research Raymond and Beverly Sackler Faeulty of Exact Sciences,
Tel Aviv University, Ramat Aviv 69978, Israel
Received 29 March 1993;revised 21 February 1995
Smoothing splines are one of the most popular approaches to nonparametric regression.
Wahba (J. Roy. Statist. Soc. Set. B 40 (1978) 364-372; 45 (1983) 133-150) showed that
smoothing splines are also Bayes estimates and used the corresponding prior model to derive
interval estimates for the regression function. Although the interval estimates work well on
a global basis, they can have poor local properties. The source of this problem is the use of
a global smoothing parameter. We introduce the notion of L k- smoothing splines. These splines
allow for a variable smoothing parameter and can substantially improve local inference.
AMS Subject Classification: 62G05, 62G15
Keywords: Bayesian linear model; Confidence interval; L-spline; Variable smoothing


Source: Abramovich, Felix - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics