An empirical Bayes derivation of best linear unbiased predictors
نویسندگان
چکیده
منابع مشابه
An Empirical Bayes Derivation of Best Linear Unbiased Predictors
Let (Y1,θ1), . . . ,(Yn,θn) be independent real-valued random vectors with Yi, given θi, is distributed according to a distribution depending only on θi for i= 1, . . . ,n. In this paper, best linear unbiased predictors (BLUPs) of the θi’s are investigated. We show that BLUPs of θi’s do not exist in certain situations. Furthermore, we present a general empirical Bayes technique for deriving BLUPs.
متن کاملBest Linear Unbiased Estimation in Linear Models
where X is a known n × p model matrix, the vector y is an observable ndimensional random vector, β is a p × 1 vector of unknown parameters, and ε is an unobservable vector of random errors with expectation E(ε) = 0, and covariance matrix cov(ε) = σV, where σ > 0 is an unknown constant. The nonnegative definite (possibly singular) matrix V is known. In our considerations σ has no role and hence ...
متن کاملA Unified Measure of Uncertainty of Estimated Best Linear Unbiased Predictors in Small Area Estimation Problems
We obtain a second order approximation to the mean squared error (MSE), and its estimate, of the empirical or estimated best linear unbiased predictor (EBLUP) of a mixed effect in a general mixed linear normal model. This covers many important small area models in the literature. Unlike previous research in this area, we provide a unified theory of measuring uncertainty of an EBLUP for a comple...
متن کاملEnhanced heritabilities and best linear unbiased predictors through appropriate blocking of progeny trials 1
In a recent article in the Canadian Journal of Forest Research (Ericsson 1997) discussed the use of postblocking in the analysis of progeny trials. We would like to comment on three aspects of this paper: The idea of postblocking a trial is well known and has been used to advantage by Patterson and Hunter (1983) as a means of studying the nature of spatial variation at trial sites. A more detai...
متن کاملAn Improved Bayes Empirical Bayes Estimator
Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2002
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s016117120211009x