On the Strong Consistency of Ridge Estimates

Abstract

In this article, we establish strong consistency of the ridge estimates using extended results for the strong consistency of the least squares estimates in multiple regression models which discard the usual assumption of null mean value for the errors and only requires them to be i.i.d. with absolute moment of order r (0 < r ⩽ 1).

Keywords:

• Least squares estimates
• Ridge regression
• Strong consistency

Mathematics Subject Classification:

• 62J07
• 60F15

Notes

a(x) = O(b(x)) as x → x₀ means that

a(x)≈b(x) as x → x₀ means that a(x) = O(b(x)) as x → x₀ and b(x) = O(a(x)) as x → x₀ i.e. a(x) is of the same order of magnitude as b(x). The notation a(x) = o(b(x)) as x → x₀ means that