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Discrete smoothing splines and digital filtration. Theory and applications

Jiří Hřebíček, František Šik, Vítězslav Veselý (1990)

Aplikace matematiky

Two universally applicable smoothing operations adjustable to meet the specific properties of the given smoothing problem are widely used: 1. Smoothing splines and 2. Smoothing digital convolution filters. The first operation is related to the data vector r = ( r 0 , . . . , r n - 1 ) T with respect to the operations 𝒜 , and to the smoothing parameter α . The resulting function is denoted by σ α ( t ) . The measured sample r is defined on an equally spaced mesh Δ = { t i = i h } i = 0 n - 1 ...

On one approach to local surface smoothing

Nikolay Dikoussar, Csaba Török (2007)

Kybernetika

A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.

Piecewise approximation and neural networks

Martina Révayová, Csaba Török (2007)

Kybernetika

The paper deals with the recently proposed autotracking piecewise cubic approximation (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can provide different local approximation models. We demonstrate how APCA can be applied to especially noisy data thanks to NN and local estimations. On the other hand,...

Seasonal time series with missing observations

Tomáš Ratinger (1996)

Applications of Mathematics

Popular exponential smoothing methods dealt originally only with equally spaced observations. When time series contains gaps, smoothing constants have to be adjusted. Cipra et al., following Wright’s approach of irregularly spaced observations, have suggested ad hoc modification of smoothing constants for the Holt-Winters smoothing method. In this article the fact that the underlying model of the Holt-Winters method is a certain seasonal ARIMA is used. Minimum mean square error smoothing constants...

SURE shrinkage of gaussian paths and signal identification

Nicolas Privault, Anthony Réveillac (2011)

ESAIM: Probability and Statistics

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

SURE shrinkage of Gaussian paths and signal identification*

Nicolas Privault, Anthony Réveillac (2012)

ESAIM: Probability and Statistics

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

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