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

Kuo-Yuan Liang, Jack Lee and Kurt Shao

Journal of Applied Statistics, 2006, vol. 33, issue 9, pages 961-973

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.

Keywords: Combining weights; critical values; error-variance minimizing criterion; inverted F-variates; Pearson Type I approximation (search for similar items in EconPapers)
Date: 2006
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