Pseudo Expectation Problem Set

In L. R. Schaeffer, Pseudo Expectation Approach to Variance Component Estimation, 1986, Journal of Dairy Science, 69, 2884-2889 an alternative estimator for variance components is described.

1. What are quadratic forms being proposed?
2. What is a "Pseudo Expectation"? What is the difference between the "Pseudo Expectation" and the actual expectation when the estimated variance are equal to the true variances?
3. In Proc IML implement the "Pseudo Expectation" approach using both the "Pseudo Expectation" and the actual expectation.
4. Return estimates of the standard errors.