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

1969/10/01 by J. V. Zidek, James V. Zidek · 3 citations
Mathematics · Decision Sciences · #Random Matrices and Applications #Probability and Risk Models #Statistical Methods and Inference

paper · pdf · doi:10.1214/aoms/1177697393

Abstract

Suppose that independent normally distributed random vectors, X^n×1 and Y^k×1, are observed with E(X) = 0, E(Y) = μ, Cov(X) = σ²I, and Cov(Y) = σ²I. It is known [2, 5] that the best invariant estimator of μ is admissible if k \leqq 2 and inadmissible if k > 2. It is also known [1, 7] that the best invariant estimator of σ is inadmissible. In this paper, these results are extended to show that the best invariant estimator of θ = Aμ + ησ, for a given matrix A and a given vector η, is inadmissible if |η| is sufficiently large (when k = 1, A = 1, θ is a quantile).

Citations

• Invariance, Minimax Sequential Estimation, and Continuous Time Processes

Cited by

• Inadmissibility of a Class of 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]

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