A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

A further note on a theorem on the difference of the generalized inverses of two nonnegative definite matrices

Andrews and Phillips (1986) gave a simplified proof for the result that established the nonnegative definiteness of the difference of the Moore-Penrose inverses of two nonoegative definite matrices, a result originally due to Milliken and Akdeniz (1977), The purpose of this paper is to offer a simple proof for a generalization of this result,     

Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective

Statistics and Computing - We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with nonlinear...     

Equalities between OLSE,BLUE and BLUP in the linear model

We consider equalities between the ordinary least squares estimator ( $\mathrm {OLSE} $ ), the best linear unbiased estimator ( $\mathrm {BLUE} $ ) and the best linear unbiased predictor ( $\mathrm {BLUP} $ ) in the general linear model $\{ \mathbf y , \mathbf X \varvec{\beta }, \mathbf V \}$ extended with the new unobservable future value $ \mathbf y _{*}$ of the response whose expectation is $ \mathbf X _{*}\varvec{\beta }$ . Our aim is to provide some new insight and new proofs for the equalities under consideration. We also collect together various expressions, without rank assumptions, for the $\mathrm {BLUP} $ and provide new results giving upper bounds for the Euclidean norm of the difference between the $\mathrm {BLUP} ( \mathbf y _{*})$ and $\mathrm {BLUE} ( \mathbf X _{*}\varvec{\beta })$ and between the $\mathrm {BLUP} ( \mathbf y _{*})$ and $\mathrm {OLSE} ( \mathbf X _{*}\varvec{\beta })$ . A remark is made on the application to small area estimation.     

Sustaining Cross-Sector Collaborations: Lessons from New Orleans

This study examines the role of faith-based and nonprofit organizations in cross-sector collaborations and the outcomes of collaborative efforts in one poverty stricken New Orleans neighborhood. The study focuses on a particular one-stop human services center that was established in the target neighborhood post-Hurricane Katrina and was tested during the aftermath of Hurricanes Gustav and Ike. The Center was evaluated during the fall of 2008, to determine whether it held up in achieving relief, recovery and rebuilding efforts, especially in relation to additional needs generated by the more recent storms. Using the Bryson et al. (2006) model of cross-sector collaboration as a beginning framework, and the subsequent expanded model of that same framework from Simo and Bies (2007), the current study examines the successes and current challenges of this particular collaborative organization, analyzes the application of the identified cross-sector collaboration models, defines the role of faith-based organizations and explores the implications for future policy and practice, as well as directions for further research in this important and under-researched area.     

Symmetry exploits for Bayesian cubature methods

Statistics and Computing - Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional...