Asymptotic normality of a variance estimator of a linear combination of a function of order statistics

Summary An estimator of the asymptotic variance of (a randomly stopped) linear combination of a function of order statistics is considered and its asymptotic normality is studied under appropriate regularity conditions. A comparative study of the regularity conditions pertaining to the asymptotic normality and strong convergence of linear combinations of functions of order statistics and their estimated asymptotic variances is also made.Research supported by the Office of Naval Research under ONR Contract N00014-79-C-0522This research is dedicated to Professor Leopold Schmetterer on the occasion of his 60th birthday