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RISK MINIMIZATION FOR TIME SERIES BINARY CHOICE WITH VARIABLE SELECTION

Published online by Cambridge University Press:  05 March 2010

Wenxin Jiang  and
Martin A. Tanner
Wenxin Jiang*
Affiliation:
Northwestern University
Martin A. Tanner
Affiliation:
Northwestern University
*
*Address correspondence to Wenxin Jiang, Department of Statistics, Northwestern University, Evanston, IL 60208, U.S.A.; e-mail: [email protected].
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Abstract

This paper considers the problem of predicting binary choices by selecting from a possibly large set of candidate explanatory variables, which can include both exogenous variables and lagged dependent variables. We consider risk minimization with the risk function being the predictive classification error. We study the convergence rates of empirical risk minimization in both the frequentist and Bayesian approaches. The Bayesian treatment uses a Gibbs posterior constructed directly from the empirical risk instead of using the usual likelihood-based posterior. Therefore these approaches do not require a correctly specified probability model. We show that the proposed methods have near optimal performance relative to a class of linear classification rules with selected variables. Such results in classification are obtained in a framework of dependent data with strong mixing.

Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 5 , October 2010 , pp. 1437 - 1452
Copyright
Copyright © Cambridge University Press 2010

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