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On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts

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Listed:
  • Kuo-Yuan Liang
  • Jack Lee
  • Kurt Shao

Abstract

This paper establishes a sampling theory for an inverted linear combination of two dependent F-variates. It is found that the random variable is approximately expressible in terms of a mixture of weighted beta distributions. Operational results, including rth-order raw moments and critical values of the density are subsequently obtained by using the Pearson Type I approximation technique. As a contribution to the probability theory, our findings extend Lee & Hu's (1996) recent investigation on the distribution of the linear compound of two independent F-variates. In terms of relevant applied works, our results refine Dickinson's (1973) inquiry on the distribution of the optimal combining weights estimates based on combining two independent rival forecasts, and provide a further advancement to the general case of combining three independent competing forecasts. Accordingly, our conclusions give a new perception of constructing the confidence intervals for the optimal combining weights estimates studied in the literature of the linear combination of forecasts.

Suggested Citation

  • Kuo-Yuan Liang & Jack Lee & Kurt Shao, 2006. "On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 961-973.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:9:p:961-973
    DOI: 10.1080/02664760600744330
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    References listed on IDEAS

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    1. Bunn, Derek W., 1985. "Statistical efficiency in the linear combination of forecasts," International Journal of Forecasting, Elsevier, vol. 1(2), pages 151-163.
    2. Lee, Jack C. & Hu, Ling, 1996. "On the distribution of linear functions of independent F and U variates," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 339-346, March.
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