On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts |
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Authors: | Kuo-Yuan Liang Jack C. Lee Kurt S. H. Shao |
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Affiliation: | a Polaris Research Institute and Department of Economics, National Taiwan University, Taiwanb National Chiao Tung University, Taiwanc Polaris Research Institute, Taiwan |
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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. |
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Keywords: | Combining weights critical values error-variance minimizing criterion inverted F-variates Pearson Type I approximation |
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