"This paper presents a new method to examine the performance evaluation of mutual funds in incomplete markets. Based on the no arbitrage condition, we develop bounds on admissible performance measures. We suggest new ways of ranking mutual funds and provide a diagnostic instrument for evaluating the admissibility of candidate performance measures. Using a monthly sample of 320 equity funds, we show that admissible performance values can vary widely, supporting the casual observation that investors disagree on the evaluation of mutual funds. In particular, we cannot rule out that more than 80% of the mutual funds are given positive values by some investors. Moreover, we empirically demonstrate that potential inference errors embedded in existing parametric performance measures can be of important magnitude." Copyright (c) 2009 The Authors Journal compilation (c) 2009 Blackwell Publishing Ltd.

Abstract.In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [4] and called Kullback-proximal algorithms. The proximal framework allows us to prove new results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space.Résumé. Le but de cet article est de proposer une analyse de l'algorithme EM du point de vue des algorithmes de point proximal. Nousétudions plus précisément un nouveau type de procedure EM généralisée introduit dans [4] et appelé algorithme Kullback proximal. Le cadre des algorithmes proximaux nous permet d'obtenir de nouveaux résultats sur les points d'accumulation. Une contribution essentielle est l'analyse détaillée du cas où un point d'accumulation est sur le bord du domaine des paramètres.

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Let X be a n × p real matrix with coherence µ(X) = max j =j ′ |X t j X j ′ |. We present a simplified and improved study of the quasi-isometry property for most submatrices of X obtained by uniform column sampling. Our results depend on µ(X), the operator norm X and the dimensions with explicit constants, which improve the previously known values by a large factor. The analysis relies on a taildecoupling argument, of independent interest, and a recent version of the Non-Commutative Chernoff inequality (NCCI).

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