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Combining two-parameter and principal component regression estimators. (English) Zbl 1416.62402

Summary: This paper is concerned with the parameter estimation in linear regression model. To overcome the multicollinearity problem, a new class of estimator, namely principal component two-parameter (PCTP) estimator is proposed. The superiority of the new estimator over the principal component regression (PCR) estimator, the \(r\)-\(k\) class estimator, the \(r\)-\(d\) class estimator and the two-parameter estimator proposed by H. Yang and X. Chang [Commun. Stat., Theory Methods 39, No. 6, 923–934 (2010; Zbl 1190.62128)] are discussed with respect to the mean squared error matrix (MSEM) criterion. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.

MSC:

62J07 Ridge regression; shrinkage estimators (Lasso)
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
62H25 Factor analysis and principal components; correspondence analysis

Citations:

Zbl 1190.62128
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References:

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