Minimax rank estimation for subspace tracking

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample covariance asymptotics stemming from random matrix theory, and bring them to bear on the problem of optimal rank estimation in the context of the standard array observation model with additive white Gaussian noise. The most significant of these results demonstrates the existence of a phase transition threshold, below which eigenvalues and associated eigenvectors of the sample covariance fail to provide any information on population eigenvalues. We then develop a decision-theoretic rank estimation framework that leads to a simple ordered selection rule based on thresholding; in contrast to competing approaches, however, it admits asymptotic minimax optimality and is free of tuning parameters. We analyze the asymptotic performance of our rank selection procedure and conclude with a brief simulation study demonstrating its practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio

The Comprehensive Longitudinal Evaluation of the Milwaukee Parental Choice Program: Summary of Fourth Year Reports

The eyes of the nation were on the state of Wisconsin, as Republican policymakers locked horns with the teachers union over reforms. The Republicans needed just one Democrat to break ranks in order for them to pass far-reaching policy changes. They finally got their wish when Representative Annette “Polly” Williams (D, Milwaukee) came over to their side. Surprised? That’s because the year was 1990, not 2011, and the farreaching policy reform was the Milwaukee Parental Choice Program (MPCP)

Law as Asymmetric Information: Theory, Application, and Results in the Context of Foreign Direct Investment in Real Estate

In his seminal 1970 article on lemon markets, George Akerlof posited the possibility of market failure in the presence of asymmetric information regarding a good’s value. In the intervening four decades, the importance of accurate valuation information has grown as transnational trade has boomed. The aim of the instant article is to assess the potential impact on transnational trade of asymmetric information regarding the legal attributes of a given good. Inaccurate or asymmetric information regarding relevant legal attributes may give rise to the same problem of market failure that Akerlof initially posited. If buyers are unsure of the ownership of a good, its conveyability, or their rights and obligations in a given transaction, they might decline to transact at all. If these legal uncertainties are pervasive, transactions in that market might cease to take place altogether. Nonetheless, consistent with the remainder of Akerlof’s article, the presence of certain counteracting institutions may lessen the impact of asymmetric information, thus forestalling market failure. These counteracting institutions in the context of asymmetric information regarding legal attributes would include a fully and fairly functioning judiciary, publicized and lucid laws and regulations, and other such mechanisms that would make clear the rights and obligations of all parties to a transaction. Thus, this article addresses the possibility of law as asymmetric information in the general sense and the specific, by assessing whether asymmetries regarding property law might contribute to market failure in the context of foreign direct investment in real estate. Regardless of whether that market is a lemons market, the conclusions of this article support systemic reform in the property regimes of developing and transition economies, to ensure that shortcomings in the institutional and legal frameworks of these states do not hinder fuller economic development

Retirement Savings Accounts: President’s Budget Proposal for FY2005

CRS ReportCRSretiresavingsprop.pdf: 243 downloads, before Oct. 1, 2020

Harvard and Yale Ascendant: The Legal Education of the Justices from Holmes to Kagan

With the nomination of Elena Kagan to be a justice of the United States Supreme Court, it is quite possible that eight of the nine justices will have graduated from only two law schools—Harvard and Yale. This article frames this development in the historical context of the legal education of those justices confirmed between 1902 and 2010. What this historical review makes clear is that the Ivy League dominance of the Supreme Court is a relatively recent occurrence whose beginnings can be traced to Antonin Scalia’s 1986 confirmation. Prior to that time, although Harvard and Yale were consistently represented among the justices, they did not constitute a majority of sitting members. In addition to this strictly historical assessment of the justices’ education, this article also attempts to ascertain why the Harvard-Yale trend has arisen, and whether this trend may have deleterious effects on the future of constitutional law. In concluding, it is the recommendation of this article that when the next vacancy arises, the President should look outside the confines of Harvard and Yale for a qualified nominee