an:01136714
Zbl 0906.62036
Shi, Peide; Zheng, Zhongguo
Multivariate resistant regression splines for estimating multivariate functions from noisy data
EN
Syst. Sci. Math. Sci. 10, No. 3, 217-224 (1997).
1000-9590
1997
j
62G07 62G20 62H12 65D07
M-estimator; nonparametric regression; multivariate resistant regression spline; tensor products of B-splines; MURRS estimator; optimal global convergence rates
Summary: The multivariate resistant regression spline (MURRS) method for estimating an underlying smooth \(J\)-variate function by using noisy data is based on approximating it with tensor products of B-splines and minimizing a sum of the \(\rho\)-functions of the residuals to obtain a robust estimator of the regression function, where the spline knots are automatically chosen through a parallel of information criterion. When the knots are deterministically given, it is proved that the MURRS estimator achieves the optimal global convergence rates established by \textit{C. J. Stone} [Ann. Statist. 13, 689-705 (1985; Zbl 0605.62065)] under some mild conditions. Examples are given to illustrate the utility of the proposed methodology. Usually, only a few tensor products of B-splines are enough to fit even complicated functions.
0605.62065