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In the paper, we present some general theorems on large deviations of random vectors with cumulants satisfying the generalized Statulevičius condition. The results obtained are applicable in derivation of limit theorems in the scheme of series, including the case where the dimension of the considered random vectors is growing indefinitely. [ABSTRACT FROM AUTHOR]

The paper is devoted to the supremum-type multivariate goodness-of-fit tests based on the empirical characteristic function. Particular attention is devoted to the composite hypothesis of normality and Gaussian distribution mixture model. An analytical way to approximate the null asymptotic distributions of the considered test statistics is discussed applying the theory of large excursions of differentiable Gaussian random fields. The produced comparative Monte Carlo power study shows that the considered tests are powerful competitors to the existing classical criteria, clearly dominating in verification of the goodness-of-fit hypotheses against the specific types of alternatives. [ABSTRACT FROM AUTHOR]

The article examines the dependencies of individual sectoral stock price indices of OMX Baltic security market on macroeconomic indicators, using econometric methods. Regression models are constructed using quarterly time series of 2000–2011 years while the methodology is backed with the findings of Lithuanian and foreign scientists from an extensive overview of specific literature. Regression equations, obtained in the paper, allows us to identify the key macroeconomic and global indicators that statistically significantly affect the Baltic securities market and to quantify their impact on the stock price indices of individual sectors in the Baltic countries. Econometric analysis of OMX Baltic security market proves the hypothesis that the set of macroeconomic regressors may vary considerably depending on the individual sector's price indices, especially in the case of small open economy with immature stock markets. The paper provides investors who are shaping their portfolios taking into account the macroeconomic forecasts with additional opportunities on the basis of sectoral stock price indices regression equations. [ABSTRACT FROM AUTHOR]

The paper is devoted to goodness of fit tests based on probability density estimates generated by kernel functions. The test statistic is considered in the form of maximum of the normalized deviation of the estimate from its expected value or a hypothesized distribution density function. A comparative Monte Carlo power study of the investigated criterion is provided. Simulation results show that the proposed test is a powerful competitor to the existing classical criteria testing goodness of fit against a specific type of alternative hypothesis. An analytical way for establishing the asymptotic distribution of the test statistic is proposed, using the theory of high excursions of close to Gaussian random processes and fields introduced by Rudzkis (1992, 2012). [ABSTRACT FROM AUTHOR]

Let { ξ( t) , t ∈ T} be a differentiable (in the mean-square sense) Gaussian random field with E ξ( t) ≡ 0, D ξ( t) ≡ 1, and continuous trajectories defined on the m-dimensional interval $ T \subset {\mathbb{R}^m} $. The paper is devoted to the problem of large excursions of the random field ξ. In particular, the asymptotic properties of the probability P = P{ −v( t) < ξ( t) < u( t) , t ∈ T}, when, for all t ∈ T, u( t) , v( t) ⩾ χ, χ → ∞, are investigated. The work is a continuation of Rudzkis research started in [R. Rudzkis, Probabilities of large excursions of empirical processes and fields, Sov. Math., Dokl., 45(1):226-228, 1992]. It is shown that if the random field ξ satisfies certain smoothness and regularity conditions, then P = e + Qo(1), where Q is a certain constructive functional depending on u, v, T, and the matrix function R( t) = cov( ξ′( t) , ξ′( t)). [ABSTRACT FROM AUTHOR]

The problem of automatic classification of scientific texts is considered. Methods based on statistical analysis of probabilistic distributions of scientific terms in texts are discussed. The procedures for selecting the most informative terms and the method of making use of auxiliary information related to the terms positions are presented. The results of experimental evaluation of proposed algorithms and procedures over real-world data are reported. [ABSTRACT FROM AUTHOR]

This paper discusses a soft sample clustering problem for multivariate independent random data satisfying the mixture model of the Gaussian distribution. The theory recommends to estimate the parameters of model by the maximum likelihood method and to use “plug‐in” approach for data clustering. Unfortunately, the calculation problem of the maximum likelihood estimate is not completely solved in multivariate case. This work proposes a new constructive a few stage procedure to solve this task. This procedure includes statistical distribution analysis of a large number of the univariate projections of observations, geometric clustering of a multivariate sample and application of EM algorithm. The results of the accuracy analysis of the proposed methods is made by means of Monte‐Carlo simulation. [ABSTRACT FROM AUTHOR]