Akahira, Masafumi Second order asymptotic properties of the generalized Bayes estimators for a family of non-regular distributions. (English) Zbl 0737.62026 Statistical theory and data analysis II, Proc. 2nd Pac. Area Stat. Conf., Tokyo/Jap. 1986, 87-100 (1988). Show indexed articles as search result. Summary: [For the entire collection see Zbl 0732.00018.]The asymptotic density of the generalized Bayes estimator, up to the second order, i.e., the order \(n^{-1}\), is given for a family of truncated distributions, and the upper bound for concentration probability for 3/2th order asymptotically median unbiased estimators is obtained, up to the 3/2th order, i.e., the order \(n^{-1/2}\), in the case of symmetrically truncated densities. It is noted that the sum and the difference of unilateral differential coefficients of the density at extreme points, with the Fisher information, affect the second order asymptotic behaviour of estimators. Cited in 3 Documents MSC: 62F15 Bayesian inference 62F12 Asymptotic properties of parametric estimators Keywords:asymptotic density; generalized Bayes estimator; family of truncated distributions; upper bound for concentration probability; asymptotically median unbiased estimators; symmetrically truncated densities; differential coefficients; extreme points; Fisher information; second order asymptotic behaviour Citations:Zbl 0732.00018 PDFBibTeX XMLCite \textit{M. Akahira}, in: Statistical theory and data analysis II, Proc. 2nd Pac. Area Stat. Conf., Tokyo/Jap. 1986, . 87--100 (1988; Zbl 0737.62026)