Statistica Sinica

Jin Mingzhong and Chen Xiru

Abstract:Let . Suppose that the random errors e_{1}e_{2}are i.i.d., with a common distributionFbelonging to the class for some . In this paper we obtain a sufficient condition for the strong consistency of the Least Sequares Estimate (LSE) of . The condition is necessary in the following sense: If the condition is not satisfied, then for some , rails to converge a.s. to .

Key words and phrases:Least squares estimate, linear models, strong consistency.