|標題:||On the distribution of the inverted linear compound of dependent F-variates and its application to the combination of forecasts|
Lee, Jack C.
Shao, Kurt S. H.
National Chiao Tung University
Department of Information Management and Finance
|關鍵字:||combining weights;critical values;error-variance minimizing criterion;inverted F-variates;Pearson Type I approximation|
|摘要:||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.|
|期刊:||JOURNAL OF APPLIED STATISTICS|