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Title:Asymptotic properties of model selection procedures in linear regression PDF Logo
Authors:Droge, Bernd
Issue Date:2003
Series/Report no.:Discussion papers of interdisciplinary research project 373 2003,28
Abstract:In regression analysis there is typically a large collection of competing models available from which we want to select an appropriate one. This paper is concerned with asymptotic properties of procedures for selecting linear models, which are based on certain data-dependent criteria such as Mallows´ Cp, cross-validation and the generalized information criterion. We avoid the assumption of an adequate ("correct") model and allow the maximal model dimension to increase with the sample size. General asymptotic concepts are introduced, covering the usual ones of consistency and asymptotic optimality. The focus is on conditions for penalizing the model complexity which are necessary to optain the different optimalities. For example, the consistency of a procedure is decided by the interplay between these penalties, the complexity of the class of model candidates, and some quantity describing the ability to identify "wrong" (pseudo-inadequate) models. Many results known from the literature appear as special cases or are slightly modified.
Subjects:Model selection
prediction
asymptotic optimality
consistency
Persistent Identifier of the first edition:urn:nbn:de:kobv:11-10050287
Document Type:Working Paper
Appears in Collections:Discussion Papers, SFB 373, HU Berlin

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