Displaying similar documents to “Geometry of the nonlinear regression with prior.”

The LASSO estimator: Distributional properties

Rakshith Jagannath, Neelesh S. Upadhye (2018)

Kybernetika

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The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behaviour. The finite sample distribution of the LASSO estimator has been previously studied for the special case of...

Using randomization to improve performance of a variance estimator of strongly dependent errors

Artur Bryk (2012)

Applicationes Mathematicae

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We consider a fixed-design regression model with long-range dependent errors which form a moving average or Gaussian process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We estimate the variance of the errors using the Rice estimator. The estimator is shown to exhibit weak (i.e. in probability) consistency. Simulation results confirm this property for moderate and large sample sizes when...

Variance components and nonlinearity

Lubomír Kubáček, Eva Tesaříková (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model....

Smoothing and preservation of irregularities using local linear fitting

Irène Gijbels (2008)

Applications of Mathematics

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For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.