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The oracle property of model selection procedures has attracted a large volume of favorable publications in the literature, but also faced criticisms of being ineffective and misleading in applications. Such criticisms, however, have appeared to be largely ignored by the majority of the popular statistical literature, despite their serious impact. In this paper, we present a new type of Hodges' estimators that can easily produce model selection procedures with the oracle and some other desired properties, but can be readily seen to perform poorly in parts of the parameter spaces that are fixed and independent of sample sizes. Consequently, the merits of the oracle property for model selection as extensively advocated in the literature are questionable and possibly overstated. In particular, because the mathematics employed in this paper are at an elementary level, this finding leads to new discoveries on the merits of the oracle property and exposes some overlooked crucial facts on model selection procedures. [ABSTRACT FROM AUTHOR]

In the present paper we derive lower asymptotic information bounds of Cramér-Rao type for estimators of nonparametric statistical functionals. The results are based on dense differentiability and dense regularity concepts which lead to weak assumptions. As explicit examples L-estimators are treated. In addition a new rapid method for the treatment of survival functionals under randomly right censored data is presented. For instance, for the famous Kaplan-Meier and Nelson-Aalen estimators, our information bound is just the lower bound obtained earlier in the literature. [ABSTRACT FROM AUTHOR]

Using a new method based on generalized sections of feasible sets, we obtain optimality conditions for vector optimization of objective multifunctions with multivalued constraints. [ABSTRACT FROM AUTHOR]

In the framework of locally convex topological vector spaces, we establish a scalarization theorem, a Lagrange multiplier theorem and duality theorems for superefficiency in vector optimization involving nearly subconvexlike set-valued maps. [ABSTRACT FROM AUTHOR]

In the framework of normed spaces, Borwein and Zhuang introduced superefficiency and gave its concise dual form when the underlying decision problem is convex. In this paper, we consider four different generalizations of the Borwein and Zhuang superefficiency in locally convex spaces and give their concise dual forms for convex vector optimization. When the ordering cone has a base, we clarify the relationship between Henig efficiency and the various kinds of superefficiency. Finally, we show that whether the four kinds of superefficiency are equivalent to each other depends on the normability of the underlying locally convex spaces. [ABSTRACT FROM AUTHOR]

It is widely recognized that general practitioners (GPs) play a key role in determining the use of resources for ambulatory care. In addition to the GPs' working hours, these resources consist of the work of specialists and that of hospital physicians treating the GPs' referrals and the cost of medication and other measures induced by the GP. Different systems of remuneration differ in their power to lead to efficient service provision. This contribution provides empirical evidence on the efficiency of service provision by Austrian GPs. The analysis is based on data for some 600 GPs. The data comprise sufficient information to assess the GPs' efficiency with regard to the way they manage their cases. Data Envelopment Analysis, a nonparametric technique, is used to estimate the production frontier. The results suggest that almost one-half of the GPs in the sample have a relative efficiency of 0.8 or less. A Malmquist decomposition of the productivity change reveals a decline in productivity. This is due to a pronounced negative shift of the frontier whereas individual efficiency rises against the weaker benchmark of the new frontier. [ABSTRACT FROM AUTHOR]

We reduce the definitions of proper efficiency due to Hartley, Henig, Borwein, and Zhuang to a unified form based on the notion of a dilating cone, i.e., an open cone containing the ordering cone. This new form enables us to obtain a comprehensive comparison among these and other kinds of proper efficiency. The most advanced results are obtained for a special class of proper efficiencies corresponding to one-parameter families of uniform dilations. This class is sufficiently wide and includes, for example, the Hartley and Henig proper efficiencies as well as superefficiency. [ABSTRACT FROM AUTHOR]