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- Alexander Zaigraev, A. Podraza-Karakulska
- 2008

The problem of estimation of an unknown shape parameter under the sample drawn from the gamma distribution, where the scale parameter is also unknown, is considered. A new estimator, called the maximum likelihood scale invariant estimator, is proposed. It is established that both the bias and the variance of this estimator are less than that of the usual… (More)

In a homogeneous jury, in which each vote is correct with the same probability, and each pair of votes correlates with the same correlation coefficient, there exists a correlation-robust voting quota, such that the probability of a correct verdict is independent of the correlation coefficient. For positive correlation, an increase in the correlation… (More)

- Adam Jakubowski, Alexander V. Nagaev, Alexander Zaigraev
- 2004

Necessary and sufficient conditions are given for multidimensional p stable limit theorems (i.e. theorems on convergence of normalized partial sums Sn/bn of a stationary sequence of random vectors to a non-degenerate strictly p-stable limiting law μ, with 1/pregularly varying normalizing sequence bn). It is proved that similarly as in the one-dimensional… (More)

Within the framework of classical linear regression model stochastic optimal design criteria are considered. As examples a line fit model and a k-way linear fit model are taken. If the optimal design does not exist, an approach consisting in choosing the efficient design is suggested.

- ALEXANDER NAGAEV, Alexander Zaigraev
- 2005

A class of absolutely continuous distributions in R is considered. Each distribution belongs to the domain of normal attraction of an Æ-stable law. The limit law is characterized by a spectral measure which is absolutely continuous with respect to the spherical Lebesgue measure. The large-deviation problem for sums of independent and identically distributed… (More)

Univariate stable distributions arose within the context of the central limit theorem as limit laws for sums of i.i.d. random variables. Except for the gaussian laws, all the stable distributions are heavy-tailed. This explains why stable distribution models are very attractive for statisticians. The fact that stable laws are limiting says a lot about… (More)

Properties of the most familiar optimality criteria, for example A-, Dand E-optimality, are well known, but the distance optimality criterion has not drawn much attention to date. In this paper properties of the distance optimality criterion for the parameter vector of the classical linear model under normally distributed errors are investigated. DS-optimal… (More)

Within the framework of classical linear regression model integral optimal design criteria of stochastic nature are considered and their properties are established. Their limit behaviour generalizes that of the distance stochastic optimality criterion. As an example a line fit model is taken.

In a homogeneous jury, the votes are exchangeable correlated Bernoulli random variables. We derive the bounds on a homogeneous jury’s competence as the minimum and maximum probability of the jury being correct, which arise due to unknown correlations among the votes. The lower bound delineates the downside risk associated with entrusting decisions to the… (More)

Within the framework of classical linear regression model optimal design criteria of stochastic nature are considered. The particular attention is paid to the shape criterion. Also its limit behaviour is established which generalizes that of the distance stochastic optimality criterion. Examples of the limit maximin criterion are considered and optimal… (More)