The general maximum likelihood empirical Bayes (GMLEB) method has been proven to possess optimal properties and demonstrated to have superior numerical performance in the Gaussian sequence model. Although it is known that nonparametric function estimation and the Gaussian sequence models are...

Given a finite set of observed data {Xtk(ω0),Ytk(ω0)} of just one sample path at n regularly spaced time of the processes Xt and Yt satisfying dXt=a0(t)dt+a1(t)dW1(t)+a2(t)dW2(t)+dJ1(t),dYt=b0(t)dt+b1(t)dW1(t)+b2(t)dW2(t)+dJ2(t),t∈[0,T], where J1,J2 are jump process, we are to investigate a...

We consider dependence structures in multivariate time series that are characterized by deterministic trends. Results from spectral analysis for stationary processes are extended to deterministic trend functions. A regression cross covariance and spectrum are defined. Estimation of these...