Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data

The main uniform convergence results of Hansen (2008) are generalized in two directions: Data is allowed to (i) be heterogenously dependent and (ii) depend on a (possibly unbounded) parameter. These results are useful in semiparametric estimation problems involving time-inhomogenous models and/or sampling of continuous-time processes. The usefulness of these results are demonstrated by two applications: Kernel regression estimation of a time-varying AR(1) model , and the kernel density estimation of a Markov chain that has not been intialized at its stationary distribution.