Statistical experiments with persistent linear regression in the Markov random medium

TitleStatistical experiments with persistent linear regression in the Markov random medium
Publication TypeJournal Article
Year of Publication2015
AuthorsKoroliouk, DV
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.04.012
Issue4
SectionMathematics
Pagination12-17
Date Published4/2015
LanguageUkrainian
Abstract
The statistical experiments (SE) with persistent non-linear regression are considered in the discrete-continuous time $k=[Nt]$, $ 0\leq t\leq T$. The directing parameters of the regression function increments depend on the state of an embedded Markov chain in the (homogeneous in time) uniformly ergodic Markov process, which describes the states of the random medium. SE are defined by the solutions of stochastic difference equations with two components: predictive and stochastic (martingale-difference). The obtained approximation in the series scheme with series parameter $N$ (size of the sample), as $N\rightarrow \infty$, is a diffusion Ornstein–Uhlenbeck-type process. The parameters of drift and diffusion are determined by averaging over the stationary distribution of the embedded Markov chain.
Keywordslinear regression, Markov random medium
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