Asymptotic properties of model selection procedures in linear regression

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 373 Discussion Paper ; No. 2003,28

Classification and Topics

• Classification: Wirtschaft
• Subject: Model selection ; prediction ; asymptotic optimality ; consistency ; Regression ; Modell-Spezifikation ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Droge, Bernd
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
• (where): Berlin
• (when): 2003

Further information

• Handle: http://hdl.handle.net/10419/22243
• URN: urn:nbn:de:kobv:11-10050287
• Last update: 10.03.2025, 11:43 AM CET