Advertisement

Journal of Mathematical Sciences

, Volume 190, Issue 4, pp 600–605 | Cite as

Recurrent statistical experiments with persistent linear regression

  • Dmitrii V. Korolyuk
Article

Abstract

Statistical experiments with persistent linear regression are considered as normalized sums \( {S_N}(k)=\frac{1}{N}\sum\nolimits_{r=1}^N {{\delta_r}(k),\;\;k\geq 0} \), of jointly independent and identically distributed, for every \( r\geq 1 \), random variables \( {\delta_r}(k),\;\;1\leq r\leq N,\;\;k\geq 0 \), which can take two values ±1. The persistent linear regression means that the recurrence relation
$$ E\left[ {{S_N}\left( {k+1} \right)|{S_N}(k)} \right]=c-2a{S_N}(k),\;k\geq 0, $$
holds. We investigate the stable mode (equilibrium) (Theorem 2.1) and propose a stochastic approximation of statistical tests as a discrete-time autoregression process with normal perturbations (Theorem 3.1).

Keywords

Recurrent statistical tests persistent linear regression equilibrium diffusion approximation stationary distribution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Abundo, L. Accardi, and N. Rosato, ”A Markovian model for cooperative interaction in proteins,” Math. Models and Meth. in Appl. Sci., 5, No. 6, 835–863 (1995).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    M. Abundo, P. Baldi, and L. Caramellino, Some Remarks about a Markov Chain Which Models Cooperative Biological Systems, Preprint UTV, 1994.Google Scholar
  3. 3.
    Yu. V. Borovskikh and V. S. Korolyuk, Martingale Approximation, VSP, Leiden, 1997.MATHGoogle Scholar
  4. 4.
    D. Koroliuk and V. S. Koroliuk, Diffusion Approximation of Markov Chains for Cooperative Interaction in Proteins, Preprint Volterra No. 156, 1993.Google Scholar
  5. 5.
    D. Koroliuk and V. S. Koroliuk, Discrete Diffusion Model of Cooperation in Proteins, Preprint Volterra No. 170, 1994.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of Telecommunications and Global Information Space of the NAS of UkraineKievUkraine

Personalised recommendations