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ASYMPTOTIC BEHAVIORS FOR CORRELATED BERNOULLI MODEL

Part of: Limit theorems Parametric inference

Published online by Cambridge University Press:  11 July 2019

Yu Miao Open the ORCID record for Yu Miao [Opens in a new window] ,
Huanhuan Ma  and
Qinglong Yang
Yu Miao
Affiliation:
College of Mathematics and Information Science, Henan Normal University, Henan Province453007, China E-mail: [email protected]; [email protected]
Huanhuan Ma
Affiliation:
College of Mathematics and Information Science, Henan Normal University, Henan Province453007, China E-mail: [email protected]; [email protected]
Qinglong Yang
Affiliation:
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Hubei Province430073, China E-mail: [email protected]
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Abstract

We consider a class of correlated Bernoulli variables, which have the following form: for some 0 < p < 1,

$$\begin{align}{P(X_{j+1}=1 \vert {\cal F}_{j})= (1-\theta_j)p+\theta_jS_j/j,}\end{align}$$
where 0 ≤ θj ≤ 1, $S_n=\sum _{j=1}^nX_j$ and ${\cal F}_n=\sigma \{X_1,\ldots , X_n\}$. The aim of this paper is to establish the strong law of large numbers which extend some known results, and prove the moderate deviation principle for the correlated Bernoulli model.

Keywords

Bernoulli modelmartingalemoderate deviationstrong law of large numbers

MSC classification

Primary: 60F10: Large deviations
Secondary: 60F15: Strong theorems 62F12: Asymptotic properties of estimators
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 4 , October 2020 , pp. 570 - 582
Copyright
Copyright © Cambridge University Press 2019

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