Efficient computation for Whittaker–Henderson smoothing

Weinert, Howard L.

doi:10.1016/j.csda.2006.11.038

Cited by 72 publications

(42 citation statements)

References 26 publications

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“…Weinert (2007) proposed an algorithm to compute the GCV score in MATLAB. Garcia (2010) recently provided an algorithm, also written in MATLAB, that does not involve the determination of B at each iterative step of the minimisation, thus reducing the time needed for the computation.…”

Section: Solution Of the Problem Using Matricesmentioning

confidence: 99%

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An extension of the Whittaker–Henderson method of graduation

Nocon

Scott

2012

Scandinavian Actuarial Journal

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We present an outline and historical summary of the WhittakerÁHenderson method of graduation (or data smoothing), together with an extension of the method in which the graduated values are obtained by minimising a WhittakerÁHenderson criterion subject to constraints. Examples are given, using data for the global average temperature anomaly and for a set of share prices, in which the proposed method appears to give good results.

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Section: Solution Of the Problem Using Matricesmentioning

confidence: 99%

“…The case p02 is also called the HodrickÁPrescott filter; see Hodrick & Prescott (1997), who used it on data subject to business cycles. According to Weinert (2007), the HodrickÁ Prescott case (p02) is frequently used in practice.…”

Section: Introductionmentioning

confidence: 99%

An extension of the Whittaker–Henderson method of graduation

Nocon

Scott

2012

Scandinavian Actuarial Journal

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“…A penalty term P(ŷ ) is the roughness of smooth data and can be expressed as a second-order divided difference (Weinert, 2007) as…”

Section: Data Smoothingmentioning

confidence: 99%

Application of digital image cross-correlation and smoothing function to the diagnosis of breast cancer

Han

Kim

Kwon

2012

Journal of the Mechanical Behavior of Biomedical Materials

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“…Although computationally more efficient than metaheuristic methods, the approach may suffer from some degree of case-sensitivity and can therefore not ensure a truly optimal solution for general datasets. The problem of curvature extraction from raw data, particularly for the case of dense and noisy data sets, is a main topic in its own right and many methods have been proposed for tackling a wide range of applications [20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Curvature-Guided Approach for the Knot-Placement Problem in Fitted Splines

Aguilar

Elizalde

Cárdenas

et al. 2018

Journal of Computing and Information Science in Engineering

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This paper presents an adaptive and computationally efficient curvature-guided algorithm for localizing optimum knot locations in fitted splines based on the local minimization of an objective error function. Curvature information is used to narrow the searching area down to a data subset where the local error function becomes onedimensional, convex, and bounded, thus guaranteeing a fast numerical solution. Unlike standard curvature-guided methods, typically relying on heuristic rules, the novel method here presented is based on a phenomenological approach as the error function to be minimized represents geometrical properties of the curve to be fitted, consequently reducing case-sensitivity issues and the possibility of defining spurious knots. A knotreadjustment procedure performed in the vicinity of a newly created knot has the ability of dispersing knots from otherwise highly knot-populated regions, a feature known to generate undesired local oscillations. The performance of the introduced method is tested against three other methods described in the literature, each handling the knotplacement problem via a different paradigm. The quality of the fitted splines for several datasets is compared in terms of the overall accuracy, the number of knots, and the computing efficiency. It is demonstrated that the novel algorithm leads to a significantly smaller knot vector and a much lower computing time, while preserving or improving the overall accuracy.

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Efficient computation for Whittaker–Henderson smoothing

Cited by 72 publications

References 26 publications

An extension of the Whittaker–Henderson method of graduation

An extension of the Whittaker–Henderson method of graduation

Application of digital image cross-correlation and smoothing function to the diagnosis of breast cancer

An Adaptive Curvature-Guided Approach for the Knot-Placement Problem in Fitted Splines

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