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Free‐knot polynomial splines with confidence intervals
Author(s) -
Mao Wenxin,
Zhao Linda H.
Publication year - 2003
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1046/j.1369-7412.2003.00422.x
Subject(s) - mathematics , knot (papermaking) , smoothing spline , statistics , estimator , confidence interval , spline (mechanical) , smoothing , nonparametric statistics , spline interpolation , chemical engineering , engineering , bilinear interpolation , structural engineering
Summary. We construct approximate confidence intervals for a nonparametric regression function, using polynomial splines with free‐knot locations. The number of knots is determined by generalized cross‐validation. The estimates of knot locations and coefficients are obtained through a non‐linear least squares solution that corresponds to the maximum likelihood estimate. Confidence intervals are then constructed based on the asymptotic distribution of the maximum likelihood estimator. Average coverage probabilities and the accuracy of the estimate are examined via simulation. This includes comparisons between our method and some existing methods such as smoothing spline and variable knots selection as well as a Bayesian version of the variable knots method. Simulation results indicate that our method works well for smooth underlying functions and also reasonably well for discontinuous functions. It also performs well for fairly small sample sizes.