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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

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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 $1,.... In from a Poisson distribution with parameter A. Show that testing A = 3 versus A / 3 yields W 2 CM for a 3. 2. Consider a random sample r1, ..., In from an exponential distribution with parameter 0. Show that testing 0 = 3 versus 0 * 3 yields W 2 CM for 0 > 3. 3. Consider a random sample 21,..., In from a Bernoulli distribution with parameter 0. Show that for testing 0 = ; versus 0 / }. we always get W 2 CM. Show also that for testing 0 = versus 0 / 4, we get WE CM for : gas ; and W 2 CM for 0

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