Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/oxford-university-press/resistant-smoothing-using-the-fast-fourier-transform-7pqwlvLOIu
References (13)
-
P. J. Huber (1981)
Robust Statistics. -
G. S. Watson (1964)
Smooth regression analysis, 26
-
D. D. Cox (1983)
Asymptotics for M‐type smoothing splines, 11
-
P. F. Velleman, D. C. Hoaglin (1981)
Applications, Basics and Computing of Exploratory Data Analysis. -
W. Härdle, S. Marron (1985)
Optimal bandwidth selection in nonparametric kernel regression, 13
-
E. A. Nadaraya (1964)
On estimating regression, 9
-
B. Bussian, W. Härdle (1984)
Robust smoothing applied to white noise and single outlier contaminated Raman spectra, 38
-
P. Hall (1984)
Asymptotic properties of integrated square error and cross‐validation for kernel estimation of a regression function, 67
-
W. Härdle (1984)
Robust regression function estimation, 14
-
D. M. Monro (1975)
Algorithm AS83. Complex discrete fast Fourier transform, 24
-
F. Utreras (1981)
On computing robust splines and applications, 2
-
D. R. Brillinger (1977)
In Discussion of “Consistent Nonparametric Regression” by C. J. Stone, 5
-
B. W. Silverman (1982)
Kernel density estimation using the fast Fourier transform, 31
- Publisher
- Oxford University Press
- Copyright
- © Royal Statistical Society
- ISSN
- 0035-9254
- eISSN
- 1467-9876
- DOI
- 10.2307/2347850
- Publisher site
- See Article on Publisher Site
Abstract
Algorithm AS 222 By W. Hardlat Institut fiir Wirtschaftstheorie JJ. West Germany [Received March 1985. Final revision July 1986] Keywords: Kernel regression estimation; resistant smoothing; Fast Fourier Transform; Language Fortran 66 Description and Purpose Suppose {(Xj' lj)}j= 1 are two-dimensional data points and it is desired to compute the regression curve r(x) = E(YI X = x) of Y on X. The following curve estimator with kernel function K and bandwidth h (1) has been introduced by Nadaraya (1964) and Watson (1964). Brillinger (1977) pointed out the non-resistance to outliers and proposed an M-type smoother. Resistant regression estimates are desirable in data analysis as was pointed out by Velleman and Hoaglin (1981). An application of a resistant smoother to a chemical problem is described in Bussian and Hardle (1984). In this paper we present an algorithm for the one-step M-type smoother 1 1 1 n- h - L K(h- (x - Xj»y,(res j) rn(x) = r:(x) + ---",-j=-n=--1------- (2) 1 1 1 n- h - L K(h- (x - X » y,'(res ) j j j= 1 where resj = lj - r:(X and y,(u) = max{ -e, min{u, en, e > 0 is Huber's (1981) well known j)
Journal
Journal of the Royal Statistical Society Series C (Applied Statistics) – Oxford University Press
Published: Mar 1, 1987
Keywords: ; ;