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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)

- 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)

In this paper we present a new stochastic characterization of the Loewner optimality design criterion. The result is obtained by proving a generalization to the well known corollary of Anderson's theorem. Certain connections between the Loewner optimality and the stochastic distance optimality design criterion are showed. We also present applications and… (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)

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.

- 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 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)

We obtain the probability distribution of the number of successes in a sequence of correlated binary trials as a function of marginal probabilities and correlation coefficients. It is based on Bahadur's representation of the joint probability distribution of correlated binary trials, truncated to second-order correlations. We provide new results,… (More)