Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle

• 成果类型: Article
• 署名作者: Aue, Alexander; Cheung, Rex C. Y.; Lee, Thomas C. M.; Zhong, Ming
• 署名单位: University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.889022
• 发表日期: 2014
• 页码: 1241-1256
• 关键词: VARIABLE SELECTION; likelihood; shrinkage

摘要

This article proposes new model-fitting techniques for quantiles of an observed data sequence, including methods for data segmentation and variable selection. The main contribution, however, is in providing a means to perform these two tasks simultaneously. This is achieved by matching the data with the best-fitting piecewise quantile regression model, where the fit is determined by a penalization derived from the minimum description length principle. The resulting optimization problem is solved with the use of genetic algorithms. The proposed, fully automatic procedures are, unlike traditional break point procedures, not based on repeated hypothesis tests, and do not require, unlike most variable selection procedures, the specification of a tuning parameter. Theoretical large-sample properties are derived. Empirical comparisons with existing break point and variable selection methods for quantiles indicate that the new procedures work well in practice.