Improved Density Estimators for Invertible Linear Processes

Improved Density Estimators for Invertible Linear Processes

ABSTRACT The stationary density of a centered invertible linear processes can be represented as a convolution of innovation-based densities, and it can be estimated at the parametric rate by plugging residual-based kernel estimators into the convolution representation. We have shown elsewhere that a functional central limit theorem holds both in the space of continuous functions vanishing at in...

Uniformly Root-n Consistent Density Estimators for Weakly Dependent Invertible Linear Processes

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimat...

Prediction in invertible linear processes

We construct root-n consistent plug-in estimators for conditional expectations of the form E(h(Xn+1, . . . , Xn+m)|X1, . . . , Xn) in invertible linear processes. More specifically, we prove a Bahadur type representation for such estimators, uniformly over certain classes of not necessarily bounded functions h. We obtain in particular a uniformly root-n consistent estimator for the m-dimensiona...

Efficient Estimation in Invertible Linear Processes

Density Estimators for Truncated Dependent Data

In some long term studies, a series of dependent and possibly truncated lifetime data may be observed. Suppose that the lifetimes have a common continuous distribution function F. A popular stochastic measure of the distance between the density function f of the lifetimes and its kernel estimate fn is the integrated square error (ISE). In this paper, we derive a central limit theorem for t...