 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2013/o5/c/solution

For a fully specified parameter value, do not maximize within the null. Substitute

θ_{0}

directly:

Λ (θ_{0}) = 2 i \sum n_{i} lo g \frac{n _{i}}{n π _{i} ( θ _{0} )} .

Under the same regularity and large-count conditions, compare with

χ_{k - 1}^{2}

, since no null parameter has been estimated. Reject in its upper tail at the desired significance level. Fixing the parameter increases the reference degrees of freedom by one relative to part (b).

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