Consider the Method 3 estimates of 0'5 and O'~ in Example 12.9.1.

(a) Show that these are also the REML estimates.

(b) Show that the vector (Y'Y, Y'Mz Y, J'Y)' is a complete sufficient statistic for the balanced one-way random effects model.

(c) Show that the Method 3 estimates are also minimum variance unbiased estimates

(d) Find the distributions of SSTrts and SSE.

(e) Find the generalized likelihood ratio test of level Q for Ho : at = 0 versus the one-sided alternative.
Hint: Use the concepts of Section 2.5 and the methods of Example 12.4.2,