Nonnegative minimum biased quadratic estimation in the linear regression models
Journal of Multivariate Analysis
SIAM Review
Self-scaled barriers and interior-point methods for convex programming
Mathematics of Operations Research
Mixed semidefinite-quadratic-linear programs
Advances in linear matrix inequality methods in control
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
SDPPACK User''s Guide -- Version 0.8 Beta
SDPPACK User''s Guide -- Version 0.8 Beta
Nonnegative quadratic estimation and quadratic sufficiency in general linear models
Journal of Multivariate Analysis
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The problem of nonnegative quadratic estimation of a parametric function γ(β, σ) = β'Fβ + Σi = 1r fiσi2 in a general mixed linear model M{y, Xβ, V(σ)= Σi = 1r σi2Vi} is discussed. Necessary and sufficient conditions are given for y' A0y to be a minimum biased estimator for γ. It is shown how to formulate the problem of finding a nonnegative minimium biased estimator of γ as a conic optimization problem, which can be efficiently solved using convex optimization techniques. Models with two variance components are considered in detail. Some applications to one-way classification mixed models are given. For these models minimum biased estimators with minimum norms for square of expectation β2 and for σ12 are presented in explicit forms.