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Improved estimation of regression parameters when the two regression lines are parallel. (English) Zbl 1109.62042

Summary: We consider two simple multivariate regression models. Our interest is to estimate the intercept and slope vectors of one model when it is apriori suspected, but not sure, that the slope vectors of the two models may be equal. Five estimators, namely unrestricted, restricted, preliminary test, shrinkage, and positive-rule shrinkage are proposed for the estimation of intercept and slope vectors. Expressions for the biases, quadratic biases, and quadratic risks of the proposed estimators are derived. The statistical properties and relative performances of the estimators are investigated based on unbiasedness and quadratic risk criteria. It is observed that, under certain conditions, the risk of the shrinkage estimator is less than that of the maximum likelihood estimator. It is also observed that the shrinkage estimator performs better than the preliminary test estimator except in a small range of the parameter space.

MSC:

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
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