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The Correlated Gamma-Ratio Distribution in Model Evaluation and Selection

  • Panaretos, John
  • Psarakis, Stelios
  • Xekalaki, Evdokia
  • Karlis, Dimitris

The paper considers the problem of selecting one of two not necessarily nested competing regression models based on comparative evaluations of their abilities in each of two different issues: The first pertains to viewing the problem as a “best-fitting” model determination problem in the sense that a model is sought which is closest to the observed data, and utilizes some measure of the adequacy of the models to describe existing observations. The second is entirely different from the first in that it takes account of the predictive adequacy of the models. It is shown that certain test statistics can be constructed which within each of the above settings can lead to appropriate model selection procedures based on sequential comparisons of the competing models in their abilities to describe the data or to predict future observations. The null distribution of these statistics, termed as the “Correlated Gamma Ratio Distribution”, is obtained as the distribution of the ratio of two correlated gamma variates. Applications are given as well as some simulation results revealing the behaviour of the model selection procedures developed. Potential extensions of the proposed procedures are described.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6355.

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Date of creation: 08 Sep 2005
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Handle: RePEc:pra:mprapa:6355
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  1. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  2. Edward Greenberg & Robert P. Parks, 1993. "A Predictive Approach to Model Selection and Multicollinearity," Econometrics 9308001, EconWPA.
  3. James G. MacKinnon, 1983. "Model Specification Tests Against Non-Nested Alternatives," Working Papers 573, Queen's University, Department of Economics.
  4. West, K.D. & Cho, D., 1993. "The Predictive Ability of Several Models of Exchange Rate Volatility," Working papers 9317r, Wisconsin Madison - Social Systems.
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