Asymptotic Distribution of the Hildreth—Houck Estimator
Patrick W. Crockett · Journal of the American Statistical Association · 1985
Hildreth and Houck (1968) discussed a random-coefficients regression model and proposed several weighted least squares estimators with estimated weights. They conjectured that the estimators are asymptotically equivalent to the weighted least squares estimator with known weights. In this article the conjecture is verified, providing the first correct proof that Hildreth—Houck estimators are asymptotically normal. One of Hildreth and Houck's conditions is eliminated. An easily applied version of a broadly applicable theorem of Carroll and Ruppert (1982) is stated.