1975/03/01 by Charles J. Stone · 6 citations
Mathematics · Medicine · #Statistical Methods and Inference #Drug Transport and Resistance Mechanisms #Liver Disease Diagnosis and Treatment
paper · pdf · doi:10.1214/aos/1176343056
openalex publication_date 1975/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04
Consider estimators θn of the location parameter θ based on a sample of size n from θ + X, where the random variable X has an unknown distribution F which is symmetric about the origin but otherwise arbitrary. Let \mathscrF denote the Fisher information on θ contained in θ + X. We show that there is a nonrandomized translation and scale invariant adaptive maximum likelihood estimator θn of θ which doe not depend on F such that \mathscrL(n(1)/(2)(θn - θ)) → N(0, 1/\mathscrJ) as n → ∞ for all symmetric F.