Strong Consistency of Estimation of Number of Regression Variables when the Errors are Independent and Their Expectations are not Equal to Each Other

摘要

This document considers the linear regression model y sub i = x sub i B + e sub i, i = 1, 2, ..., where (x sub i) - is a sequence of known p-vectors, Beta = (Beta Sub 1, ..., Beta Sub p) is an unknown p-vector, known as regression coefficients, (e Sub i) is a sequence of random errors. It is of interest to test the hypothesis H Sub k: Beta Sub k+1 = ... = Beta Sub p = O, k = O, 1,...,p. We do not assume that the random errors are identically distributed and have zero means, since it is sometimes realistic. As a compensation for this relaxation, we assume the errors have a common bounded support A Sub 1, a Sub 2 under certain conditions, we obtain the strongly consistent estimate of the number k for which Beta Sub k is not equal to O and Beta Sub k+1 = ... = Beta Sub p = O, by using the information theoretical criteria.