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Yuri A. Kutoyants (2004)
SORT
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We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.
I. Malinowska, P. Pawlas, D. Szynal (2005)
Applicationes Mathematicae
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The minimum variance linear unbiased estimators (MVLUE), the best linear invariant estimators (BLIE) and the maximum likelihood estimators (MLE) based on m selected kth record values are presented for the parameters of the Gumbel and Burr distributions.
Masayuki Uchida, Nakahiro Yoshida (2011)
ESAIM: Probability and Statistics
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The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality...
M. Hušková (1985)
Banach Center Publications
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Masayuki Uchida, Nakahiro Yoshida (2012)
ESAIM: Probability and Statistics
Similarity:
The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic...
Ryszard Zieliński (2007)
Applicationes Mathematicae
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It turns out that for standard kernel estimators no inequality like that of Dvoretzky-Kiefer-Wolfowitz can be constructed, and as a result it is impossible to answer the question of how many observations are needed to guarantee a prescribed level of accuracy of the estimator. A remedy is to adapt the bandwidth to the sample at hand.
Jaromír Antoch, Marie Husková (2000)
Discussiones Mathematicae Probability and Statistics
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The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.