On the Distribution of the Inverted Linear Compound of Dependent F-Variates and its Application to the Combination of Forecasts
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; Pearson Type I approximation; critical values; error-variance minimizing criterion; inverted F-variates
Document Type: Research Article
Affiliations: 1: Polaris Research Institute and Department of Economics, National Taiwan University, Taiwan 2: National Chiao Tung University, Taiwan 3: Polaris Research Institute, Taiwan
Publication date: 01 November 2006
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