Moderate Deviations Principle And The Law Of The Iterated Logarithm For LSE In Linear Models

By considering Laplace asymptotical integer, we get the moderate deviations principle for the least squares estimates in linear model. We not only get the result of the errors are independent and identically distributed with valued in R~d, but also present the result when the errors are R~d—valued martingale difference. Consequently, we apply the latter result to study the errors are bounded R~d—valued φ—mixing stationary sequence and Markov chain.Besides these results, we obtain the law of the iterated logarithm for the norms of the estimates when the random errors are independent and identically distributed with valued in R~d. When the random errors are martingale difference and φ—mixing stationary sequence and Markov chain, we get the law of the iterated logarithm of each component of the estimates.