Uniform Convergence Rates of Kernel Estimators with Heterogenous, Dependent Data

The main uniform convergence results of Hansen (2008, Econometric Theory 24, 726–748) are generalized in two directions: Data are allowed to (a) be heterogeneously dependent and (b) depend on a (possibly unbounded) parameter. These results are useful in semiparametric estimation problems involving time-inhomogeneous models and/or sampling of continuous-time processes. The usefulness of these results is 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 initialized at its stationary distribution.