Simultaneous Testing and Estimation with Dependent Chi-square Random Variables

摘要

Frequently the experimenter is confronted with an analysis involving two or more Chi-square random variables. This is often the case, for example, in experimental design or regression problems. Provided the Chi-square random variables are independent, probabilities associated with the random variable are easily determined. If the Chi-square random variables are not independent the analyses are much more complex and few practical tools are currently available to the experimenter. In the report the case of two dependent Chi-square random variables is discussed. A unified approach to solving the distributional problems is presented using canonical analysis. Density functions are derived for the bivariate Chi-square random variable with a special type of dependence. From a study of moments of the distribution, an approximation for any type of dependence using the special form mentioned above is suggested. (Author)