Statistica Sinica
9(1999), 289-296
STRONG CONSISTENCY OF LEAST SQUARES
ESTIMATE IN MULTIPLE REGRESSION
WHEN THE ERROR VARIANCE IS INFINITE
Jin Mingzhong and Chen Xiru
GuiZhou National College and Graduate School, Chinese Academy
Abstract:
Let
.
Suppose that the random errors
e1e2
are i.i.d., with a common
distribution F
belonging 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.