“Informatics and Applications” scientific journal

Volume 2, Issue 2, 2008

Content   Abstract and Keywords   About Authors

NETWORK METHODS OF SEPARATION OF MIXTURES OF PROBABILITY DISTRIBUTIONS AND THEIR APPLICATION TO THE DECOMPOSITION OF VOLATILITY INDEXES

• V. Korolev. M. V. Lomonosov Moscow State University; IPI RAN, vkorolev@comtv.ru
• E. Nepomnyashchiy. 45th Central Science Research Institute, RussianMinistry of Defence
• A. Rybal'chenko. M. V. Lomonosov Moscow State University, alex-rybalchenko@yandex.ru
• A. Vinogradova. M. V. Lomonosov Moscow State University, a_nuta@mail.ru

Abstract:  Methods are proposed for the statistical separation ofmixtures of probability distributions based on theminimization of the discrepancy between the theoretical and empirical distribution functions. Main attention is paid to the minimization of sup- and L1-norms of the discrepancy. It is demonstrated that these problems can be reduced to problems of linear programming. The simplex-method is used for their numerical realization. The proposed methods are applied to the problem of decomposition of the volatility of financial indexes. Examples of the decomposition of the volatility of AMEX, CAC 40, NIKKEI, and NASDAQ indexes are presented.

Keywords: separation of mixtures of probability distributions; problem of linear programming; simplex-method; volatility

SOME STATISTICAL PROBLEMS RELATED TO THE LAPLACE DISTRIBUTION

• V. Bening  M. V. Lomonosov Moscow State University; IPI RAN, bening@yandex.ru
• V. Korolev  M. V. Lomonosov Moscow State University; IPI RAN, vkorolev@comtv.ru

Abstract: Approach proposed in Bening V., Korolev V. // Rus. J. Probability Theory and Its Applications, 2004. Vol. 49. No. 3. P. 419-435 is developed. Some grounds are given why it is natural to use the Laplace distribution in some problems of probability theory andmathematical statistics. As a statistical illustration, an application of the Laplace distribution to problems of the asymptotical testing of hypotheses is considered.

Keywords: Laplace distribution; testing of statistical hypotheses; power function; asymptotically most powerful tests

SOME BOUNDS FOR CLOSED TO ABSORBING MARKOV MODELS

• A. I. Zeifman VSPU; IPI RAN; VSCC CEMI RAS, a_zeifman@mail.ru
• A. V. Chegodaev 2VSPU, cheg_al@mail.ru
• V. S. Shorgin IPI RAN, vshorgin@ipiran.ru

Abstract: Nonstationary continuous-time Markov models with "almost absorbing" zero state are considered. Such models describe some problems of queueing theory. The properties and bounds for the limit characteristics of such models are obtained. Simple continuous-time random walks as example of considered models are also studied.

Keywords: :  queueing networks; continuous-timeMarkov chains; ergodicity; birth and death process; simple random walk

THE OPTIMIZATION OF THE SPATIAL LOCATION OF SERVICE STATIONS

• T. Zakharova M. V. LomonosovMoscow State Unisersity, lsa@cs.msu.su

Abstract: In the N-dimensional Euclidean space, service stations are being efficiently located according to the criterion of stationary average waiting time.

Keywords:  service stations location; optimality criterion; waiting time

ELIMINATION OF ECTOPIC BEATS FROMHEART TACHOGRAMUSING ROBUST ESTIMATES

• A. V.Markin.  M.V. Lomonosov Moscow State University, artem.v.markin@mail.ru
• O. V. Shestakov.  2M.V. Lomonosov Moscow State University, oshestakov@cs.msu.su

Abstract: A method of removing ectopic beats from tachogramis introduced. The method is based on authors' mathematical model. Parameters of the model are estimated using robust linear regression. Elimination of ectopic beats is made by the instrumentality of confidential intervals for RR-interval differences. Real data results are supplied and discussed.

Keywords:  tachogram; robust estimates; linear regression; confidential intervals

ON THE ASYMPTOTIC DISTRIBUTION OF THEMAXIMUMORDER STATISTIC IN A SAMPLE WITH RANDOMSIZE

• V. Pagurova  M.V. Lomonosov Moscow State University, pagurova@yandex.ru

Abstract:  The asymptotic distribution of the normalized maximum is investigated under the assumption that the random sample size is representable as a sum of n independent identically distributed random variables. This paper generalizes the results of Pagurova V. // Statistical methods of estimating and testing of hypoteses. - Perm, 2005. P. 104-113 where the sample size was Poisson-distributed with a parameter n. For a one-parameter family of distributions depending on an unknown location parameter, the rate of convergence of the distribution of the normalized maximum to the limit law is investigated. The classes of distributions with exponential and power-type tails are considered.

Keywords:  randomly indexed maximum; one-parameter family of distributions; convergence rate

ESTIMATION OF DELAY DISTRIBUTION IN BIOLOGICAL DYNAMICALMODELS WITH A MODEL OF HIV INFECTION AS AN EXAMPLE

• A.N. Ushakova  Norwegian University of Science and Technology, anastasi@math.ntnu.no

Abstract:  Two methods for estimating a delay distribution in biological dynamical systems are presented. The model of HIV infection serves as an example of such a system. The first method is based on parametric approach and approximation of the delay density by a gamma-density. The second method is nonparametric and is based on solution of a convolution equation with selection of the regularization parameter either fromthemeasurement error estimated beforehand, or from the smoothness of the delay distribution.

Keywords:  dynamical systems with delay; distribution of delay; regularization parameter.

EXISTENCE OF CONSISTENT TEST SEQUENCES AT THE COMPLEX NULL HYPOTHESES IN DISCRETE STATISTICAL PROBLEMS

• A. Grusho. Russian State Humanitarian University; M.V. Lomonosov Moscow State University, grusho@yandex.ru
• E. Timonina. Russian State Humanitarian University, eltimon@yandex.ru
• V. Chentsov3. IPI RAN, ipiran@ipiran.ru

Abstract:  The problem of existence of a consistent test sequence is considered for testing of complex hypothesis against complex alternatives in a sequence of finite spaces. When the sequence of spaces is generated by Cartesian product of a finite set and probability measures on these spaces are consistent, it is possible to find sufficient conditions of existence of consistent test sequence in terms of topological properties of the certain sets. Under additional conditions it is possible to refuse the requirement of domination of certain measures from a null hypothesis and uniform limitation of density.

Keywords:  consistent test sequence; complex hypothesis against complex alternatives; finite spaces; probability measures; sufficient conditions

STOCHASTIC EXPANSIONS OF UNBIASED ESTIMATORS FOR THE CASE OF ONE-PARAMETER EXPONENTIAL FAMILY

• V. Chichagov. Perm State University, chvv50@mail.ru

Abstract:  Asymptotic and stochastic expansions are obtained for all unbiased estimators which can be constructed from a repeated sample of independent identically distributed random variables having one and the same distribution from a one-parameter exponential family. A comparison is conducted of expansions of unbiased estimators with those of maximum likelihood estimators. A stochastic expansion is obtained for an unbiased estimator of the variance of an unbiased estimator.

Keywords:  unbiased estimator; exponential family; stochastic expansion; unbiased estimator of variance