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
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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...
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.
Sergey Tarima, Dmitri Pavlov (2005)
ESAIM: Probability and Statistics
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In many practical situations sample sizes are not sufficiently large and estimators based on such samples may not be satisfactory in terms of their variances. At the same time it is not unusual that some auxiliary information about the parameters of interest is available. This paper considers a method of using auxiliary information for improving properties of the estimators based on a current sample only. In particular, it is assumed that the information is available as a number of...
M. Ivette Gomes, Lígia Henriques-Rodrigues (2010)
Discussiones Mathematicae Probability and Statistics
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In this article, we begin with an asymptotic comparison at optimal levels of the so-called "maximum likelihood" (ML) extreme value index estimator, based on the excesses over a high random threshold, denoted PORT-ML, with PORT standing for peaks over random thresholds, with a similar ML estimator, denoted PORT-MP, with MP standing for modified-Pareto. The PORT-MP estimator is based on the same excesses, but with a trial of accommodation of bias on the Generalized Pareto model underlying...
Christine H. Müller (2000)
Discussiones Mathematicae Probability and Statistics
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For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared...
Adès, Michel, Dion, Jean-Pierre, MacGibbon, Brenda (2005)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 60J60, 62M99. In this paper, we study the quasi-likelihood estimator of the drift parameter θ in the Ornstein-Uhlenbeck diffusion process, when the process is observed at random time points, which are assumed to be unobservable. These time points are arrival times of a Poisson process with known rate. The asymptotic properties of the quasi-likelihood estimator (QLE) of θ, as well as those of its approximations are also elucidated....