Noncompatible estimation of the residuai sum of sguares of central limit theorem in linear model

Abstract:

      in linear models, the error varianceσ2 of random errors is usually estimat-ted by the residual sum of squares (divided by a su ita ble degree of free-dom), based on the first n observation, (denote it by σ_n²). it is well known t that under certain conditions, the distribution of this estimate, when standardised, converges to the standard normal distribution. In this paper, it is shown that |G_n(x)-Ф(x)|=O(n^-δ/2(1+|x|)^-(2+δ)). when the errors are indepedent (maynot be identically distributed) and their 4 + 2δ order moments exist, where G_n(x) is the distribution of (σ_n²-σ²/(varσ_n²)^1/2,Ф(x)=1/(2π)^1/2∫_-∞^xe^-r2/2dt.