Alexander Zaigraev

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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)
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)
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)
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)