Fourier methods for model selection

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• 作者：M. D. Jiménez-Gamero ; A. Batsidis…
• 关键词：Empirical characteristic function ; Model selection ; Misspecified models
• 刊名：Annals of the Institute of Statistical Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：68
• 期：1
• 页码：105-133
• 全文大小：664 KB
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• 作者单位：M. D. Jiménez-Gamero (1)
  A. Batsidis (2)
  M. V. Alba-Fernández (3)
  
  1. Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes, s.n., 41012, Sevilla, Spain
  2. Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece
  3. Departamento de Estadística e Investigación Operativa, Universidad de Jaén, Campus de Las Lagunillas, Edificio Ciencias Experimentales y de la Salud, 23071, Jaén, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Netherlands
• ISSN：1572-9052

文摘

A test approach to the model selection problem based on characteristic functions (CFs) is proposed. The scheme is close to that proposed by Vuong (Econometrica 57:257–306, 1989), which is based on comparing estimates of the Kullback–Leibler distance between each candidate model and the true population. Other discrepancy measures could be used. This is specially appealing in cases where the likelihood of a model cannot be calculated or even, if it has a closed expression, it is either not easily tractable or not regular enough. In this work, the closeness is measured by means of a distance based on the CFs. As a prerequisite, some asymptotic properties of the minimum integrated squared error estimators are studied. From these properties, consistent tests for model selection based on CFs are given for separate, overlapping and nested models. Several examples illustrate the application of the proposed methods. Keywords Empirical characteristic function Model selection Misspecified models