15.4 Technical appendix
In this section we give the precise conditions under which the bound (15.4) holds.
Define:
furthermore let
denote the elements of
.
For some positive constants
and for
consider
the random set were the following conditions are fulfilled:
Let
obey (15.1), where the
regressors are possibly stochastic, then it holds holds for the estimate
:
A proof of this statement can be found in Liptser and Spokoiny (1999). For a further generalization,
where the hypothesis of local time homogeneity holds only approximatively, see Härdle et al. (2000).