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In this paper, we obtain the central limit theorems for LS estimator in simple linear errors-in-variables (EV) regression models under some mild conditions. And we also show that those conditions are necessary in some sense.

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In this paper, we consider the linear autoregressive model with varying coefficients θn∈[0,1). When θn tending to the unit root, the moderate deviation principle for empirical covariance is discussed, and as statistical applications, we provide the moderate deviation estimates of the least square and the Yule–Walker estimators of the parameter θn.