Partial Coherence Estimation via Spectral Matrix Shrinkage under Quadratic Loss

Partial coherence is an important quantity derived from spectral or precision matrices and is used in seismology, meteorology, oceanography, neuroscience and elsewhere. If the number of complex degrees of freedom only slightly exceeds the dimension of the multivariate stationary time series, spectral matrices are poorly conditioned and shrinkage techniques suggest themselves. When true partial coherencies are quite large then for shrinkage estimators of the diagonal weighting kind it is shown empirically that the minimization of risk using quadratic loss (QL) leads to oracle partial coherence estimators superior to those derived by minimizing risk using Hilbert-Schmidt (HS) loss. When true partial coherencies are small the methods behave similarly. We derive two new QL estimators for spectral matrices, and new QL and HS estimators for precision matrices. In addition for the full estimation (non-oracle) case where certain trace expressions must also be estimated, we examine the behaviour of three different QL estimators, the precision matrix one seeming particularly robust and reliable. For the empirical study we carry out exact simulations derived from real EEG data for two individuals, one having large, and the other small, partial coherencies. This ensures our study covers cases of real-world relevance

Ensemble estimation of polarization ellipse parameters

Accepted versio

Statistical properties of the estimated degree of polarization

Published versio

Attenuation estimation from correlated sequences

Published versio

A variance equality test for two correlated complex Gaussian variables with application to spectral power comparison

Published versio

Avoiding Death by Discussion Board: Asynchronous Online Chats in Aviation History

Universities and colleges are increasingly turning to online course offerings, especially in aviation education. Faculty are increasingly asked to turn their in-person courses into online flavors. Typically, faculty are creating online courses with discussion boards to mimic the scholarly community that exists in a face-to-face classroom. Faculty often create discussion boards, with varying degrees of effectiveness, to provide for the immersion of community. However, the actual effectiveness of discussion boards is debated in recent research. This research examines Asynchronous Online Chats as a replacement for the Death by Discussion Board model. Data from the past two semesters will be examined from an Aviation History course taught at the undergraduate level at the collegiate and university level. Survey instruments used include: Community of Online Learning Patterns of Adaptive Learning Social Achievement Goal

Carbon Dioxide Reduction Systems

The Methoxy system for regenerating oxygen from carbon dioxide was studied. Experiments indicate that the reaction between carbon dioxide and hydrogen can be carried out with ease in an efficient manner and with excellent heat conservation. A small reactor capable of handling the C02 expired by three men has been built and operated. The decomposition of methane by therma1,arc and catalytic processes was studied. Both the arc and catalytic processes gave encouraging results with over 90 percent of the methane being decomposed to carbon and hydrogen in some of the catalytic processes. Control of the carbon deposition in both the catalytic and arc processes is of great importance to prevent catalyst deactivation and short circuiting of electrical equipment. Sensitive analytical techniques have been developed for all of the components present in the reactor effluent streams