On Threshold Estimation in Threshold Regression Models

• Activity Number: 570
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Friederike Greb*+ and Tatyana Krivobokova and Axel Munk and Stephan von Cramon-Taubadel
• Companies: University of Goettingen and Georg-August-Universitaet Goettingen and University of Goettingen and University of Goettingen
• Keywords: threshold regression model ; threshold estimation ; Bayesian estimator ; empirical Bayes ; nuisance parameters

Abstract

Estimation of threshold parameters in various threshold regression models is typically performed by maximizing the corresponding profile likelihood. However, in certain situations such estimator performs poorly. For example, the threshold estimator can be seriously biased if the true threshold divides the data into sets of very unequal sizes and many nuisance parameters are present. A natural solution would be to employ a Bayesian estimator (BE). BEs have been considered in the literature. In particular, in an i.i.d. setting asymptotic optimality results, which are independent of priors, have been proven for BEs. Yet we find that the choice of priors can crucially affect estimation results in small samples and non-informative priors can distort estimates. In contrast, with an adequate parametrization and selection of priors we are able to regularize nuisance parameter estimates. Using an empirical Bayes method, we obtain the penalty coefficients in a data-driven manner. Simulation results show that this produces an estimator which performs well even in situations where commonly used estimators fail. We illustrate the relevance of our approach with several real-data examples.