Estimators of slopes in linear errors-in-variables regression models when the predictors have known reliability matrix

DOI10.1016/0167-7152(93)90005-4zbMath0792.62057OpenAlexW2044067321MaRDI QIDQ1802433

Leon Jay Gleser

Publication date: 26 July 1994

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(93)90005-4

zbMATH Keywords

maximum likelihood estimatorsignal-to-noise ratioleast squares estimatorpredictorsminimax estimatorreliability matrixlinear shrinkagematrix lossrandom regressorsequivariant estimationbest unbiased estimatorestimation of slopesbounded slopeserror-prone measurementlinear errors-in- variables regression modellinearly inadmissibletotal mean-squared-error risktotal squared-error loss

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Admissibility in statistical decision theory (62C15)

Related Items (14)

On the usefulness of knowledge of error variances in the consistent estimation of an unreplicated ultrastructural model ⋮ Generalized fiducial inference in the multiple regression model with measurement errors ⋮ Restricted estimation in multivariate measurement error regression model ⋮ Coefficient of determination for multiple measurement error models ⋮ Using stochastic prior information in consistent estimation of regression coefficients in replicated measurement error model ⋮ Consistent estimation of regression coefficients in ultrastructural measurement error model using stochastic prior information ⋮ Weighted Stochastic Restricted Estimation in Linear Measurement Error Models ⋮ Goodness of fit in restricted measurement error models ⋮ Confidence Interval Estimation in Ultrastructural Model ⋮ Replicated measurement error model under exact linear restrictions ⋮ Restricted estimation and testing of hypothesis in linear measurement errors models ⋮ On the estimation of the linear relation when the error variances are known ⋮ Use of prior information in the consistent estimation of regression coefficients in measurement error models ⋮ On Liu-type biased estimators in measurement error models

Cites Work

• Unnamed Item
• Unnamed Item
• Estimating linear statistical relationships
• Minimax risk over hyperrectangles, and implications
• The nonexistence of \(100(1-\alpha)\%\) confidence sets of finite expected diameter in errors-in-variables and related models
• Estimating a bounded normal mean
• Minimax estimation of the mean of a normal distribution when the parameter space is restricted
• Estimation in a multivariate errors in variables regression model: Large sample results
• Estimation of parameters in a linear model
• An ancillarity paradox which appears in multiple linear regression
• The Importance of Assessing Measurement Reliability in Multivariate Regression
• Uniform Approximation of Minimax Point Estimates

This page was built for publication: Estimators of slopes in linear errors-in-variables regression models when the predictors have known reliability matrix