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Equivariant estimation of a normal mean using a normal concomitant variable for covariance adjustment
Author(s) -
Berry J. Calvin
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315207
Subject(s) - estimator , equivariant map , mathematics , mean squared error , covariance , bivariate analysis , multivariate normal distribution , statistics , correlation coefficient , random variable , multivariate statistics , pure mathematics
Equivariant point estimators of one component of a bivariate normal mean vector are considered when the second component is known. Equivariant point estimators are characterized and compared in terms of their risk functions with respect to a normalized squared‐error loss function. Specific point estimators that dominate the usual estimator when the squared correlation coefficient is sufficiently large are provided.