We consider finite-state time-nonhomogeneous Markov chains whose transition matrix at time n is I+G/n<SUP><FONT FACE="Symbol">z</FONT></SUP> where G is a ``generator'' matrix, that is G(i,j)0 for i,j distinct, and G(i,i)= -∑<SUB>k<FONT FACE="Symbol">≠</FONT>i</SUB> G(i,k), and <FONT FACE="Symbol">z</FONT>0 is a strength parameter. In these chains, as time grows, the positions are less and...</font></font></sub></font></sup>

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Using the new inequality we obtain tight bounds for empirical loss minimization learning.

This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed which allow for endogeneities in the nonstationary regressors and serial dependence in the shocks that...