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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. [ABSTRACT FROM AUTHOR]

In this article, we consider the following simple linear errors-in-variables (EV) model: and obtain the asymptotic normality of the least square (LS) estimators for the unknown parameters β, θ in the above EV model under the assumptions that the errors are positively associated stationary sequences. [ABSTRACT FROM AUTHOR]