Inadmissibility of a Class of Estimators of a Normal Quantile

1971/08/01 by James V. Zidek · 3 citations
Mathematics · Decision Sciences · #Statistical Methods and Inference #Probability and Risk Models

paper · pdf · doi:10.1214/aoms/1177693258

Abstract

Suppose that independent normally distributed random vectors W^{n× 1} and T^{k× 1} are observed with E(W) = 0, E(T) = μ, Cov (W) = σ² I and Cov (T) = σ² I. In this paper it is shown that each member of a certain class of estimators of μ + ησ for a given vector η is inadmissible if loss is dimension-free quadratic loss. This class includes the best invariant estimator. The proof is carried out by exhibiting, for each member, θ, of the class, an estimator depending on θ whose risk is uniformly smaller than that of θ.

Citations

• Inadmissibility of the Best Invariant Estimator of Extreme Quantiles of the Normal Law Under Squared Error Loss

Cited by

• A class of minimax estimators of a normal quantile
• The appropriateness of Bland-Altman's approximate confidence intervals for limits of agreement. [europepmc]
• Comparison of alternative approaches for difference, noninferiority, and equivalence testing of normal percentiles. [europepmc]

Related

• Inadmissibility of the Best Invariant Estimator of Extreme Quantiles of the Normal Law Under Squared Error Loss
• Admissible estimators of a multivariate normal mean vector when the scale is unknown
• A universal robustification procedure
• A sharp boundary for SURE-based admissibility for the Normal means problem under unknown scale
• Efficient Estimation of Quantiles in Missing Data Models