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The restricted and unrestricted two-parameter estimators. (English) Zbl 1129.62051

Summary: We introduce a new two-parameter estimator by grafting the contraction estimator into the modified ridge estimator proposed by B. F. Swindel [ibid. 5, 1065–1075 (1976; Zbl 0342.62035)] (1976). This new two-parameter estimator is a general estimator which includes the ordinary least squares, the ridge, the K. Liu [ibid. 22, No. 2, 393–402 (1993; Zbl 0784.62065)], and the contraction estimators as special cases. Furthermore, by setting restrictions \(R\beta = r\) on the parameter values we introduce a new restricted two-parameter estimator which includes the well-known restricted least squares, the restricted ridge proposed by J. Groß [Stat. Probab. Lett. 65, No. 1, 57–64 (2003; Zbl 1116.62368)], the restricted contraction estimators, and a new restricted Liu estimator which we call the modified restricted Liu estimator different from the restricted Liu estimator proposed by S. Kaçıranlar et al. [Sankhyā, Ser. B 61, 443–459 (1999)]. We also obtain necessary and sufficient conditions for the superiority of the new two-parameter estimator over the ordinary least squares estimator and the comparison of the new restricted two-parameter estimator to the new two-parameter estimator is done by the criterion of matrix mean square error. The estimators of the biasing parameters are given and a simulation study is done for the comparison as well as the determination of the biasing parameters.

MSC:

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
62F30 Parametric inference under constraints
62J07 Ridge regression; shrinkage estimators (Lasso)
62F10 Point estimation
65C05 Monte Carlo methods
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