Question: (Testing on the Boundary) The Student distribution contains the normal as a special case, suggesting that one can construct hypothesis test statistics for normality with

(Testing on the Boundary) The Student distribution contains the normal as a special case, suggesting that one can construct hypothesis test statistics for normality with this generalization. Suppose that {(%): 1., N) are i.i.d. Using the information in Exercise 15.18,

(a) create a score test for

Y-XBo Ho N(0, 1)~1x against the alternative hypothesis that H:

(b) argue that the Wald and LR tests do not possess approximately chi-square distributions under Ho, and

(c) explain why the score test does not suffer from this difficulty.

Y-XBo Ho N(0, 1)~1x against the alternative hypothesis that H:

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