An empirical process central limit theorem for dependent non-identically distributed random variables
The author proves a central limit theorem for empirical processes indexed by functions in the weakly dependent case. The underlying observations have to be near epoch dependent on strongly mixing random variables, a condition satisfied by functions of strongly mixing sequences. The class of functions has to satisfy some smoothness condition, allowing a series expansion with uniformly summable coefficients. In detail functions on a bounded subset of \(R^ k\) with a uniformly bounded Sobolev norm are treated. As an example the author studies the asymptotic normality of a weighted least squares estimator in a nonlinear time series model.
central limit theorem for empirical processes
scientific article; zbMATH DE number 4211158
scientific article