Precise Asymptotics of Error Variance Estimator in Partially Linear Models

<正>In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression models, yi = xiτβ+ g(ti) +εi, 1≤i≤n, {εi,i = 1,…, n} are i.i.d random errors with mean 0 and positive finite varianceσ2. Following the ideas of Allan Gut and Aurel Spatarut and Zhang, on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.