Detection of outliers by the Chauvenet test in observations connected in a homogeneous Markov chain

Let x₁, ..., x_n be random variables, connected in a normal Markov chain. The paper investigates the asymptotic behavior when n of the distribution of the random variable N, equal to the number of outliers in the Chauvenet sense.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 163–169, 1989.     

Detection of gross errors in observation results with the aid of the Chauvenet test

One gives the asymptotic distribution of the number N of gross observations, rejected by the Chauvenet method, for random variables with distribution function containing an unknown parameter, when as the estimator of the unknown parameter one makes use of the maximum likelihood estimator.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 153–159, 1986.In conclusion, I express my gratitude to I. A. Ibragimov for his interest in the problem and for his remarks.     

Some asymptotic results associated with the chauvenet test for multidimensional random variables

The article presents some results associated with the asymptotic properties of the Chauvenet test for multidimensional random variables.     

Central limit theorem for centered frequencies of a countable ergodic markov chain

On the basis of results concerning the behavior of the potential of a countable ergodic Markov chain for a certain class of functions, the asymptotic normality of the variable is proved. The asymptotic normality of centered frequencies is obtained without using the condition of finiteness of the timeM ₀² of the first return to a chain state.Deceased.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1713–1715, December, 1993.     

Estimating mean time to absorption for a markov chain with limited information

In many applications of absorbing Markov chains, solution of the problem at hand involves finding the mean time to absorption. Moreover, in almost all real world applications of Markov chains, accurate estimation of the elements of the probability matrix is a major concern. This paper develops a technique that provides close estimates of the mean number of stages before absorption with only the row sums of the transition matrix of transient states.     

On the scheme of rare events for a homogeneous Markov chain

We analyze the asymptotic behavior of a homogeneous, Markov chain with discrete time under a certain scheme of rare events. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.     

Compatibility of multi-wave panel data and the continuous-time homogeneous Markov chain. An analysis of a continuous-time process by means of discrete-time longitudinal observations

Multi-wave panel data are observations at two or more points in time on a continuously changing attribute of interest (e.g. behaviour). In this paper, the adequacy of the continuous-time homogeneous Markov chain (CTHMC) model is assessed for describing the process of change underlying such data. In the case of equidistant observational times, it may happen that the maximum-likelihood estimate of the transition probability matrix between successive observational times from these data cannot arise from a CTHMC. It is investigated whether this event can be ascribed to chance through the introduction of an hypothesis test. © 1998 John Wiley & Sons, Ltd.     

Solution of a singular homogeneous Hilbert boundary-value problem for analytic function in multiply connected circular domain

We offer a new approach for solving the homogeneous Riemann-Hilbert boundary-value problem for analytic function in multiply connected circular domains. The approach is based on determination of analytic function in terms of known boundary values of its argument in a special case.     

Boundary-value problems for sums of random variables,defined on a countably-valued markov chain. II

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 590–597, May, 1989.     

A test for detecting the outlying observations in a multivariate normal family

One presents a test for the detection of outlaying observations in the multivariate normal case; it is a generalization of a test due to Bol'shev [1], intended for the one-dimensional case.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 176–180, 1980.     

On a problem of linear extrapolation for homogeneous and isotropic random fields from the observations on a circle

We shall find a linear extrapolation formula for a homogeneous and isotropic plane random field which is observed on n concentric circles. Necessary and sufficient conditions are given for error-free extrapolation of a field with respect to a circle to its center.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 589–598, November, 1968.In concluding the author thanks M. I. Yadrenko for posing the problem and for help during the work.