cosine of angle ij θ between the vectors . i j x and x An arbitrary real symmetric matrix, Q (defined above), is not a genuine product moment correlation matrix obtainable from some real X although it may appear to be so. Such negative semidefinite (nsd) or pseudocorrelation matrices may enter into empirical investigation due to several reasons. First, the coefficients of correlation may not be...

A bstract-We discuss the problem of testing for constant versus time varying regression coefficients. Our alternative hypothesis allows the coefficients to follow a stationary AR(1) process with unknown autoregressive parameter. Standard testing procedures are inappropriate since this parameter is identified only under the alternative. We propose a test statistic which is a function of a sequen...

This paper develops the empirical likelihood (EL) inference on parameters and baseline function in a semiparametric nonlinear regression model for longitudinal data in the presence of missing response variables. We propose two EL-based ratio statistics for regression coefficients by introducing the working covariance matrix and a residual-adjusted EL ratio statistic for baseline function. We es...

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This pro...

this paper studies the sequential sampling scheme, as a solution to the problem of aliasing, where the sampling interval is restricted to a minimum allowable value d t. in the sequential sampling, the signal is sampled at intervals of d t, d t+ dt , d t+2 dt , d t+3 dt , ...; where dt < d t and may be selected as desirable. the sequential sampling is, however, analyzed and it is proven that, wh...

This paper introduces an approach for flexible, robust Bayesian modeling of structure in spherical data sets. Our method is based upon a recent construction called the needlet, which is a particular form of spherical wavelet with many favorable statistical and computational properties. We perform shrinkage and selection of needlet coefficients, focusing on two main alternatives: empirical-Bayes...

Empirical Bayes methods are privileged in data mining because they can absorb prior information on model parameters and are free of choosing tuning parameters. We proposed an iterated conditional modes/medians (ICM/M) algorithm to implement empirical Bayes selection of massive variables while incorporating sparsity or more complicated a priori information. The algorithm is constructed on the ba...

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions

Mean glandular dose (MGD) is the main dosimetric quantity in mammography. MGD evaluation is obtained by multiplying the entrance skin air kerma (ESAK) by normalized glandular dose (DgN) coefficients. While ESAK is an empirical quantity, DgN coefficients can only be estimated with Monte Carlo (MC) methods. Thus, a MC parameters benchmark is needed for effectively evaluating DgN coefficients. GEA...

The Relevance Vector Machine (RVM) provides an empirical Bayes treatment of function approximation by kernel basis expansion. In its original form ?, RVM achieves a sparse representation of the approximating function by structuring a Gaussian prior distribution in a way that implicitly puts a sparsity pressure on the coefficients appearing in the expansion. RVM aims at retaining the tractabilit...