Asymptotic Local Minimaxity in Sequential Point Estimation

Asymptotic Optimality in Sequential interval Estimation

Beginning with Stein’s [9] two stage procedure, there has been substantial interest in the use of sequential methods to set a fixed width confidence interval for the mean of a distribution with unknown variance. This interest was stimulated by the fully sequential procedures of Anscombe [l] and Chow and Robbins [2] for the normal and non-parametric cases, and continues today. The recent work of...

On Nonparametric Sequential Point Estimation

Minimaxity in Estimation of Restricted Parameters

This paper is concerned with estimation of the restricted parameters in location and/or scale families from a decision-theoretic point of view. A simple method is provided to show the minimaxity of the best equivariant and unrestricted estimators. This is based on a modification of the known method of Girshick and Savage (1951) and can be applied to more complicated cases of restriction in the ...

Asymptotic Minimaxity of Wavelet Estimators with Sampled Data

Donoho and Johnstone (1997) studied a setting where data were obtained in the continuum white noise model and showed that scalar nonlinearities applied to wavelet coefficients gave estimators which were asymptotically minimax over Besov balls. They claimed that this implied similar asymptotic minimaxity results in the sampleddata model. In this paper we carefully develop and fully prove this im...

Minimaxity in predictive density estimation with parametric constraints

This paper is concerned with estimation of a predictive density with parametric constraints under Kullback-Leibler loss. When an invariance structure is embedded in the problem, general and unified conditions for the minimaxity of the best equivariant predictive density estimator are derived. These conditions are applied to check minimaxity in various restricted parameter spaces in location and...