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Combining the Liu estimator and the principal component regression estimator. (English) Zbl 1009.62560
Summary: In this paper we introduce a class of estimators which includes the ordinary least squares (OLS), the principal components regression (PCR) and the Liu estimator (1). In particular, we show that our new estimator is superior, in the scalar mean-squared error (mse) sense, to the Liu estimator, to the OLS estimator and to the PCR estimator.

MSC:
62J07 Ridge regression; shrinkage estimators (Lasso)
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[1] DOI: 10.1080/03610929308831027 · Zbl 0784.62065
[2] DOI: 10.2307/1267352 · Zbl 0202.17206
[3] DOI: 10.2307/1267351 · Zbl 0202.17205
[4] Stein, C. 1956. Inadmissibility of usual estimator for the mean of a multivariate normal distribution. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. 1956, Berkeley. pp.197–206. University of California Press.
[5] DOI: 10.1080/03610929508831585 · Zbl 0937.62612
[6] Gruber M. H.J., Improving Efficiency by Shrinkage: The James Stein and Ridge Regression Estimators (1998) · Zbl 0920.62085
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[10] DOI: 10.1080/03610928408828675
[11] DOI: 10.1080/03610928508829057 · Zbl 0592.62063
[12] Hald A., Statistical Theory with Engineering Applications (1952) · Zbl 0048.36404
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