Covariance matrix estimation with heterogeneous samples

We consider the problem of estimating the covariance matrix Mp of an observation vector, using heterogeneous training samples, i.e., samples whose covariance matrices are not exactly Mp. More precisely, we assume that the training samples can be clustered into K groups, each one containing Lk, snapshots sharing the same covariance matrix Mk. Furthermore, a Bayesian approach is proposed in which the matrices Mk. are assumed to be random with some prior distribution. We consider two different assumptions for Mp. In a fully Bayesian framework, Mp is assumed to be random with a given prior distribution. Under this assumption, we derive the minimum mean-square error (MMSE) estimator of Mp which is implemented using a Gibbs-sampling strategy. Moreover, a simpler scheme based on a weighted sample covariance matrix (SCM) is also considered. The weights minimizing the mean square error (MSE) of the estimated covariance matrix are derived. Furthermore, we consider estimators based on colored or diagonal loading of the weighted SCM, and we determine theoretically the optimal level of loading. Finally, in order to relax the a priori assumptions about the covariance matrix Mp, the second part of the paper assumes that this matrix is deterministic and derives its maximum-likelihood estimator. Numerical simulations are presented to illustrate the performance of the different estimation schemes

Endometrial injury in women undergoing assisted reproductive techniques

ACKNOWLEDGEMENTS We would like to express our appreciation to Dra Abha Maheshwari for her important authorial contribution to the previous version of this review. We also acknowledge the important help provided by the Cochrane Menstrual Disorders and Subfertility Group team, specially by Marian Showell, Trials Search Co-ordinator; by Helen Nagels, Managing Editor; and by Prof. Cindy Farquhar, Co-ordinating Editor. Finally, we would like to express our gratitude to the following investigators, who provided essential information for the preparation of this review: TK Aleyamma, Erin F Wolff, Lukasz Polanski, Nava Dekel, Neeta Singh, Suleyman Guven and Tracy YeungPeer reviewedPublisher PD

Making monetary policy: what do we know and when do we know it?

President Anthony Santomero points out that conducting a successful monetary policy presents real-world challenges, such as evaluating where the economy is, where it is going, and where it should be going. But how do monetary policymakers make decisions about the economy in a world with imperfect information? Santomero discusses how policymaking is affected by both the availability and reliability of economic information. He concludes that given the information constraints policymakers face, the challenges of setting monetary policy will not go away, so we must find a way to meet themMonetary policy

A Stochastic Bioeconomic Model with Research

This paper provides an incremental extension of a stochastic renewable resource model (Pindyck 1984) to include population dynamics research; i.e., the rate of accrual of information regarding the stochastic evolution of the stock, as a dynamic choice variable. While Pindyck models variance in stock growth as an exogenous parameter, our formulation endogenizes this variance and characterizes the impact of scientific information accrual on both the harvest decision and the present value of rents resulting from harvest activity. We illustrate the theoretical existence of an internal optimum in research effort using a numerical example.stochastic bioeconomic model, stochastic control, fisheries management, population dynamics research, renewable resource, uncertainty, Resource /Energy Economics and Policy, Q2, Q22, C61,