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Bosworth, Ken W.; Lall, Upmanu

LOWLAD: A locally weighted \(L_ 1\) smoothing spline algorithm with cross validated choice of smoothing parameters. (English) Zbl 0828.65010

Numer. Algorithms 9, No. 1-2, 85-106 (1995).
The authors explore to extend the nonparametric estimator known as the \(L_1\) or least absolute deviations (LAD) smoothing spline to situations where a locally “windowed” robust smoother, similar to the lowest smoother of W. S. Cleveland, S. J. Devlin and E. Grosse [J. Econometrics 37, No. 1, 87-114 (1988; M.R. 89a:62157)] is called for. Complementing this windowed smoothing spline is a cross validation (CV) score which allows the data at hand to select the proper degree of smoothing within the local window, and to select the proper size window.
An algorithm scheme, coupling the computation of the local LAD smoothing spline with the CV-dictated optimal choice of the smoothing parameters is presented. For background material on smoothing splines see for example G. Wahba [Spline models for observational data, CBMS-NSF Regional Conference Series in Applied Mathematics, 59, Philadelphia, PA: SIAM, XII (1990; Zbl 0813.62001)].
Reviewer: H.P.Dikshit (Jabalpur)

MSC:

65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
65C99 Probabilistic methods, stochastic differential equations
62J05 Linear regression; mixed models

Keywords:

robust regression; smoothing and regression splines; least absolute deviations smoothing spline; choice of smoothing parameters; cross validation

Citations:

Zbl 0813.62001

Software:

GAMS; FSQP; LINPACK; NPSOL; LOWLAD
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\textit{K. W. Bosworth} and \textit{U. Lall}, Numer. Algorithms 9, No. 1--2, 85--106 (1995; Zbl 0828.65010)
Full Text: DOI

References:

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