An approximation to the distribution of the ratio of two general quadratic forms with application |
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Authors: | Brajendra C Sutradhar Roy F Bartlett |
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Institution: | Department of Mathematics and Statistics , Memorial University of Newfoundland , St. John's, Newfoundland, AlC 5S7, Canada |
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Abstract: | Based on mixed cumulants up to order six, this paper provides a four moment approximation to the distribution of a ratio of two general quadratic forms in normal variables. The approximation is applied to calculate the percentile points of modified F-test statistics for testing treatment effects when standard F-ratio test is misleading because of dependence among observations. For the special case, when data is generated by an AR(1) process, the approximation is evaluated by a simulation study. For the general SARMA (p,q)(P,Q)s process, a modified F-test statistic Is given, and its distribution for the (0,1)(0,l)12 process, is approximated by the moment approximation technique. |
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Keywords: | Ratio of two general quadratic forms First four moments Johnson curves Hypothesis testing Correlated data Modified F-test statistics |
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