CIS (Current Index to Statistics)

Here we deal with the following question: Is it true that, for any closed interval on the real line R that does not contain the origin, there exists a characteristic function f such that f(x) coincides with the normal characteristic function e−x2/2 on this interval but f(x) 6≡ e−x2/2 on R? The answer to this question is positive. We study a more general case of an arbitrary characteristic function g of a continuous probability density, instead of e−x2/2.

Rough set theory has been used extensively in fields of complexity, cognitive sciences, and artificial intelligence, especially in numerous fields such as expert systems, knowledge discovery, information system, inductive reasoning, intelligent systems, data mining, pattern recognition, decision-making, and machine learning. Rough sets models, which have been recently proposed, are developed applying the different fuzzy generalisations. Currently, there is not a systematic literature review and classification of these new generalisations about rough set models.Therefore, in this review study, the attempt is made to provide a comprehensive systematic review of methodologies and applications of recent generalisations discussed in the area of fuzzy-rough set theory. On this subject, the Web of Science database has been chosen to select the relevant papers. Accordingly, the systematic and metaanalysis approach, which is called “PRISMA,” has been proposed and the selected articles were classified based on the author and year of publication, author nationalities, application field, type of study, study category, study contribution, and journal in which the articles have appeared. Based on the results of this review, we found that there are many challenging issues related to the different application area of fuzzy-rough set theory which can motivate future research studies.

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.

The article examines the dependencies of individual sectoral stock price indices of OMX Baltic security market on sectoral indicators of Lithuania economy, using econometric methods. Regression models are constructed using quarterly time series of 2005–2013 years. VAR models obtained in the [3] paper have been extended to verify if the inclusion of sectoral economy indicators improves the ability to provide a higher level of accuracy in estimating the growth of sectoral price index. These indicators significantly improve the predictive power compared with the benchmark VAR model. The short-term forecasts of the investigated models are obtained. Econometric analysis of OMX Baltic security market proves the hypothesis that the set of sectoral regressors may vary considerably depending on the individual sector’s price indices.

The aim of the present paper was to increase the efficiency of self-tuning minimum variance (MV) control of linear systems followed by the so-called hard nonlinearities. To this end, an approach based on reordering of observations to be processed for the reconstruction of an unmeasurable internal intermediate signal, which acts between a linear dynamic time-invariant (LTI) system and a static nonlinear block of the closed loop Wiener system with a saturation nonlinearity in an output, has been developed. The technique based on the ordinary least squares and on data partition is used for the internal signal extraction. The results of numerical simulation, identification, and self-tuning MV control as well as generalized MV control of the second-order discrete-time closed loop LTI system with the saturation nonlinearity are given by the computer.

Daugelis taikomųjų uždavinių naudoja nepilnai apibrėžtus duomenis. Tai būdinga ekspertų vertinimams, kai neapibrėžtumo šaltinis yra jų subjektyvumas. Neapibrėžtumo įtaka gali būti įvertinta skirtingais būdais, taikant neraiškiųjų skaičių teorijos bei matematinės statistikos metodus. Straipsnyje siūlomas Bajeso metodo taikymas, kai ilgametei kurso vertinimo patirčiai ir ekspertų vertinimo paklaidai taikomi skirtingų skirstinių deriniai. Rezultatai iliustruojami vertinant nuotolinio kurso kokybę.

A number of new formulas and an asymptotic expansion for the Euler–Mascheroni constant γ not containing logarithm are obtained. The accuracy of approximations for the constant by the partial sums of the asymptotic expansion is evaluated. It is conceivable that these formulas and the asymptotic expansion will be helpful in working out algorithms for high-precision computation of the constant in shortening the computation time and in analysis of the irrationality of the constant γ.

In this paper, we extend the results obtained in [J. Sunklodas, Some estimates of normal approximation for the distribution of a sum of a random number of independent random variables, Lith. Math. J., 52(3):326–333, 2012] for a thrice-differentiable function h : R - R to the case of h [...] BL(R); namely, we estimate the quantity [...] where h is a real bounded Lipschitz function, Zn = (Sn - ESn) / [...], Sn = X1 + ... + Xn , X1, X2, ... are independent, not necessarily identically distributed, real random variables, N is a positive integer-valued r.v. independent of X1, X2, ..., and Y is a standard normal random variable.

In this paper, we address the problem of an efficient estimation strategy when solving real survey sampling problems. We consider the panel data model with random effects as a superpopulation model. We investigate the performance of model-assisted estimators under model-based sample designs in a simulation experiment based on the real data (Lithuanian survey on short-term statistics on service) taken as a true population. Here the model-based sampling refers to a sample design constructed using the model and information about the behavior of the model-assisted estimator on available auxiliary data.

Design-based and design-based model-assisted estimator of total for a variable having many zero values has high variance. The censored regression (tobit) model-based estimators of a finite-population total have been proposed earlier. The aim of the current research is to apply the semiparametric model to a variable with many zero values, to estimate the population total by model-based and model-assisted estimators, and to compare them with other known estimators by simulation.