0000000000359036

AUTHOR

Götz Trenkler

showing 2 related works from this author

Minimax estimation with additional linear restrictions - a simulation study

1988

Let the parameter vector of the ordinary regression model be constrained by linear equations and in addition known to lie in a given ellipsoid. Provided the weight matrix A of the risk function has rank one, a restricted minimax estimator exists which combines both types of prior information. For general n.n.d. A two estimators as alternatives to the unfeasible exact minimax estimator are developed by minimizing an upper and a lower bound of the maximal risk instead. The simulation study compares the proposed estimators with competing least-squares estimators where remaining unknown parameters are replaced by suitable estimates.

Statistics and ProbabilityMathematical optimizationRank (linear algebra)Modeling and SimulationLinear regressionStatisticsEstimatorMinimax estimatorMinimaxEllipsoidUpper and lower boundsLinear equationMathematicsCommunications in Statistics - Simulation and Computation
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Linear and ellipsoidal restrictions in linear regression

1991

The problem of combining linear and ellipsoidal restrictions in linear regression is investigated. Necessary and sufficient conditions for compactness of the restriction set are proved assuring the existence of a minimax estimator. When the restriction set is not compact a minimax estimator may still exist for special loss functions arid regression designs

Statistics and ProbabilityPolynomial regressionStatistics::TheoryMathematical optimizationProper linear modelLinear predictor functionBayesian multivariate linear regressionLinear regressionLinear modelPrincipal component regressionStatistics Probability and UncertaintySimple linear regressionMathematicsStatistics
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