Estimating functions of location and scale of t -distribtion
Dale Edward Umbach · Journal of nonparametric statistics · 1994
The problem of optimally selecting a few, say k, order statistics from a sample of size n from a location-Scale family of t distributions for estimating sufficiently smooth functions, say g(λ, δ) of the location and scale parameters is considered. First, the asymptotically best linear estimators of λ and δ say, , are obtained for a fixed spacing of the order statistics. These are then used to estimate g(λ, δ) With . A lower bound for the efficiency of this estimator is introduced, which is independent of g. This lower bound is maximized to obtain the conservative spacings. The results of the maximization are presented in tables for k = 2, 3, 4, and 5, with degrees of freedom 1, 2, 3, 5, 10, 20, and ∞.