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- A. Zaigraev, A. Podraza-Karakulska
- 2008

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Abstract The problem of estimation of an unknown shape parameter under the sample… (More)

Properties of the most familiar optimality criteria, for example AD D-and 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)

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 S n /b n of a stationary sequence of random vectors to a non-degenerate strictly p-stable limiting law µ, with 1/p-regularly varying normalizing sequence b n). It is proved that similarly as in the… (More)

- ALEXANDER NAGAEV, ALEXANDER ZAIGRAEV
- 2005

A class of absolutely continuous distributions in R d is considered. Each distribution belongs to the domain of normal attraction of an AE-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… (More)

Within the framework of classical linear regression model stochas-tic 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.

- A. Zaigraev
- 2006

A class of multidimensional α-stable distributions is considered. The Poisson spectral measure of each distribution is assumed to be absolutely continuous with respect to the surface Lebesgue measure. The author concentrates his attention on the asymptotic behavior of the α-stable densities s(x) as |x| → ∞ and |x| → 0.

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)

- A. Zaigraev, A. Podraza-Karakulska
- 2014

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Maximum integrated likelihood estimator of the interest parameter when the nuisance… (More)

- Alexander Zaigraev, Magdalena Alama-Bućko
- 2011

institutional repository or funder's repository and make it publicly available immediately. Abstract Given a large sample from a location-scale population we estimate the unknown parameters by means of confidence regions constructed on the basis of two order statistics. The problem of the best choice of those statistics to obtain good estimates, as n → ∞,… (More)