An elementary development of the equation characterizing best linear unbiased estimators
نویسندگان
چکیده
منابع مشابه
The equalities of ordinary least-squares estimators and best linear unbiased estimators for the restricted linear model
We investigate in this paper a variety of equalities for the ordinary least-squares estimators and the best linear unbiased estimators under the general linear (Gauss-Markov) model {y, Xβ, σΣ} and the restrained model {y, Xβ |Aβ = b, σΣ}.
متن کاملSome properties of the best linear unbiased estimators in multivariate growth curve models
The purpose of this article is to build a class of the best linear unbiased estimators (BLUE) of the linear parametric functions, to prove some necessary and sufficient conditions for their existence and to derive them from the corresponding normal equations, when a family of multivariate growth curve models is considered. It is shown that the classical BLUE known for this family of models is t...
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 کاملAn 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 کاملElementary Estimators for High-Dimensional Linear Regression
We consider the problem of structurally constrained high-dimensional linear regression. This has attracted considerable attention over the last decade, with state of the art statistical estimators based on solving regularized convex programs. While these typically non-smooth convex programs can be solved by the state of the art optimization methods in polynomial time, scaling them to very large...
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: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00396-3