On Fourier coefficient estimators consistent in the mean-square sense

Waldemar Popiński

Displaying similar documents to “On Fourier coefficient estimators consistent in the mean-square sense”

Modified power divergence estimators in normal models – simulation and comparative study

Iva Frýdlová, Igor Vajda, Václav Kůs (2012)

Kybernetika

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Point estimators based on minimization of information-theoretic divergences between empirical and hypothetical distribution induce a problem when working with continuous families which are measure-theoretically orthogonal with the family of empirical distributions. In this case, the $φ$ -divergence is always equal to its upper bound, and the minimum $φ$ -divergence estimates are trivial. Broniatowski and Vajda [3] proposed several modifications of the minimum divergence rule to provide a solution...

Admissible invariant estimators in a linear model

Czesław Stępniak (2014)

Kybernetika

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Let $𝐲$ be observation vector in the usual linear model with expectation $𝐀 β$ and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic $𝐚^{T} 𝐲$ is called invariant estimator for a parametric function $φ = 𝐜^{T} β$ if its MSE depends on $β$ only through $φ$ . It is shown that $𝐚^{T} 𝐲$ is admissible invariant for $φ$ , if and only if, it is a BLUE of $φ,$ in the case when $φ$ is estimable with zero variance, and it is of the form $k \hat{φ}$ , where $k \in 〈0, 1〉$ and $\hat{φ}$ is an arbitrary BLUE, otherwise. This result...

One Bootstrap suffices to generate sharp uniform bounds in functional estimation

Paul Deheuvels (2011)

Kybernetika

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We consider, in the framework of multidimensional observations, nonparametric functional estimators, which include, as special cases, the Akaike–Parzen–Rosenblatt kernel density estimators ([1, 18, 20]), and the Nadaraya–Watson kernel regression estimators ([16, 22]). We evaluate the sup-norm, over a given set $𝐈$ , of the difference between the estimator and a non-random functional centering factor (which reduces to the estimator mean for kernel density estimation). We show that, under...

Some measures of the amount of information for the linear regression model.

Mihoc, Ion, Fătu, Cristina–Ioana (2008)

Acta Universitatis Apulensis. Mathematics - Informatics

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A central limit theorem for random fields.

Fazekas, István, Chuprunov, Alexey (2004)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Limit distribution of the integrated squared error of trigonometric series regression estimator.

Nadaraya, E. (1994)

Georgian Mathematical Journal

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An efficient estimator for Gibbs random fields

Martin Janžura (2014)

Kybernetika

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An efficient estimator for the expectation $\int f P ̣$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.