Admissible predictive density estimation

Let $X|\mu\sim N_p(\mu,v_xI)$ and $Y|\mu\sim N_p(\mu,v_yI)$ be independent $p$-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on observing $X=x$, we consider the problem of estimating the true predictive density $p(y|\mu)$ of $Y$ under expected Kullback--Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang [Statistical Decision Theory and Related Topics (1982) III 205--230] are sufficient for a formal Bayes rule to be admissible.Comment: Published in at http://dx.doi.org/10.1214/07-AOS506 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Counterrevolution?--National Criminal Law After Raich

This article provides an in-depth analysis of the Supreme Court’s recent decision in Gonzales v. Raich. The Court rejected by a margin of 6-3 a Ninth Circuit holding that the federal Controlled Substances Act would probably be found unconstitutional as applied to intrastate users of marijuana who were in conformity with California’s Compassionate Use Act. Although the majority, and Justice Scalia concurring, found the case to present a relatively straightforward problem in the application of Commerce Clause doctrine, the three dissenters (Justice O’Connor, joined by Chief Justice Rehnquist, and Justice Thomas) sounded sharp notes decrying a betrayal of New Federalism principles as well as an abandonment of United States v. Lopez and United States v. Morrison. The article begins with a detailed analysis of the four different opinions that the case generated in the Supreme Court, as well as a look at the Ninth Circuit decision. This decision’s willingness to prefer state law over federal, as well as the strong federalism themes of the dissent, represent an important data point in any overall consideration of where national power under the Commerce Clause is headed. The article also devotes substantial attention of the use by Justices Stevens and Scalia of Wickard v. Filburn. Wickard, with its aggregation principle, has long been a sore point for conservatives. However, no Justice in Raich called for its overruling, and the Wickard-based analysis of class of activities statutes emerged stronger than ever. The second section of the article discusses the potential impact of Raich on the current Court’s New Federalism initiative, or perhaps initiatives. I contend that to adopt the view of the Ninth Circuit would have constituted a substantial advance of that set of precepts. However, the fact that Raich came out the way it did does not necessarily constitute a rollback for the New Federalism. In particular, Justice Stevens’ insistence on the need for an economic/commercial subject of regulation as the overall test of validity of statutes with a purported effect on interstate commerce represents a reaffirmation of Lopez and Morrison. The open question is whether his lack of reference to the non-attenuation or noninfinity arguments of the majority in those cases represents any form of retreat. In the third section I consider some implications of Raich for the federal criminal law. The article presents the case as vindicating the view that the American system will continue to be noteworthy for the presence of two largely overlapping sets of criminal statutes. The article also examines specific issues such as the use of jurisdictional elements, as-applied challenges, and the reach of federal criminal law at the outer boundaries of national authority. The cases involving federal prosecution for child pornography are used to illustrate this latter problem as well as to provide a further elucidation of the general discussion of the current status of federal criminal laws, particularly those passed under the Commerce Clause

Beyond the New Federalism: Revenue Sharing in Perspective

In 1972 Congress added General Revenue Sharing to the list of federal grant-in-aid programs for states and localities. President Nixon had recommended Revenue Sharing, as apart of his New Federalism, because it would foster local autonomy by minimizing federal restrictions on the grants. When General Revenue Sharing was renewed in 1976, Congress made no changes in the formula, leading some commentators to minimize the significance of those changes which were made. Professor Brown argues that the 1976 renewal amendments to the Revenue Sharing Act are an example of interventionist federalism, a new form of federal influence over state and local governments. The federal government, while not specifying how Revenue Sharing funds must be spent, places on recipients strict conditions meant to promote such policies as non-discrimination and open access to state and local decision-making bodies. Thus the 1976 amendments, while enhancing local autonomy in spending decisions, enable the federal government to affect state administration in a potentially broader way than in the past

An Introduction to the Community Development Litigation and Its Impact

Paper from Advisory Committee on Intergovernmental Relations Conference on Federal Grant Law held December 12, 1979 in Washington, D.C