Qn 103

Qn 104

Berndt and Savin in 1977 showed that W 2 CR 2 CM for the case of a multivariate regression model with normal disturbances. Ullah and Zinde-Walsh in 1984 showed that this inequality is not robust to non-normality of the disturbances. In the spirit of the latter article, this problem considers simple examples from non-normal distributions and illustrates how this conflict among criteria is affected. 1. Consider a random sample 21, . .., In from a Poisson distribution with parameter A. Show that testing A = 3 versus A # 3 yields W 2 CM for 2 5 3 and WS CM for 2 2 3. 2. Consider a random sample 21, . ... In from an exponential distribution with parameter 9. Show that testing # = 3 versus # # 3 yields W 2 CM for 0