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Displaying similar documents to “A central limit theorem for random fields.”

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...

An efficient estimator for Gibbs random fields

Martin Janžura (2014)

Kybernetika

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An efficient estimator for the expectation ∫ 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.

Asymptotic behaviour of a transport equation

Ryszard Rudnicki (1992)

Annales Polonici Mathematici

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We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation u t + b u x + c u = a ∫ 0 a x u ( t , a x - y ) μ ( d y ) . We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.