Improving Penalized Least Squares through Adaptive Selection of Penalty and Shrinkage

Estimation of the mean function in nonparametric regression is usefully separated into estimating the means at the observed factor levels—a one-way layout problem—and interpolation between the estimated means at adjacent factor levels. Candidate penalized least squares (PLS) estimators for the mean vector of a one-way layout are expressed as shrinkage estimators relative to an orthogonal regression basis determined by the penalty matrix. The shrinkage representation of PLS suggests a larger class of candidate monotone shrinkage (MS) estimators. Adaptive PLS and MS estimators choose the shrinkage vector and penalty matrix to minimize estimated risk. The actual risks of shrinkage-adaptive estimators depend strongly upon the economy of the penalty basis in representing the unknown mean vector. Local annihilators of polynomials, among them difference operators, generate penalty bases that are economical in a range of examples. Diagnostic techniques for adaptive PLS or MS estimators include basis-economy plots and estimates of loss or risk.     

A Product Theorem for Markov Chains with Application to PF-Queueing Networks

Queueing networks in random environments represent more realistic models of computer and telecommunication systems than classical product form networks. This is due to the fact that network behaviour often depends on human activities which may vary according to daytime dependent behavioural patterns as well as physiological and mental indexes. In this paper we establish a product connection theorem for Markov chains which contains some corresponding results for spatial processes as well as for queueing networks in random environment as special cases. We demonstrate how our results can be applied to construct an adequate model for wireless networks with hook up capacity.     

Spectral image analysis for the absorption bands of the beta-methallyl free radical in the vapor phase

The radicals formed in the flash photolysis of 2-methylbut-1-ene and subsequent reactions have been investigated by kinetic spectroscopy and gas liquid chromatography. Less than 10% of photo products are formed by a molecular made of fission of the excited olefin, and of the radical modes the relative probabilities of band fission, beta(CH):beta(CH):alpha(CC) are 13:1.37:1. The extinction coefficients of beta-methallyl radical measured experimentally for all the absorption bands. The decay of the beta-methallyl radical was second order. The rate constant for the beta-methallyl radical recombination experimentally measured was 2.6+/-0.3 x 10(10) l mol(-1)s(-1) at 295+/-2K. The spectrum image showing the absorption bands was examined by image processing techniques in order to improve the visual experience of each band by localizing to a specific region of interest. Experimental results illustrate how the exact location of absorption bands was clearly extracted from the spectral image and further improvements in the visual detection of absorption bands.