Li, Yalian; Yang, Hu A new ridge-type estimator in stochastic restricted linear regression. (English) Zbl 1283.62145 Statistics 45, No. 2, 123-130 (2011). Summary: In this paper, we propose a new ridge-type estimator called the weighted mixed ridge estimator by unifying the sample and prior information in linear model with additional stochastic linear restrictions. The new estimator is a generalization of the weighted mixed estimator [B. Schaffrin and H. Toutenburg, Z. Angew. Math. Mech. 70, No. 6, 735–738 (1990; Zbl 0714.62061)] and ordinary ridge estimator (ORE) [A. E. Hoerl and R. W. Kennard, Technometrics 12, 55–67 (1970; Zbl 0202.17205)]. The performances of this new estimator against the weighted mixed estimator, ORE and the mixed ridge estimator [Y. Li and H. Yang, Stat. Pap. 51, No. 2, 315–323 (2010; Zbl 1247.62179)] are examined in terms of the mean squared error matrix sense. Finally, a numerical example and a Monte Carlo simulation are also given to show the theoretical results. Cited in 19 Documents MSC: 62J05 Linear regression; mixed models 62J07 Ridge regression; shrinkage estimators (Lasso) Keywords:weighted mixed ridge estimator; ordinary ridge estimator; weighted mixed estimator; mixed ridge estimator; mean squared error matrix Citations:Zbl 0714.62061; Zbl 0202.17205; Zbl 1247.62179 PDFBibTeX XMLCite \textit{Y. Li} and \textit{H. Yang}, Statistics 45, No. 2, 123--130 (2011; Zbl 1283.62145) Full Text: DOI References: [1] Stein C., Proceedings of the Third Berkley Symposium on Mathematical and Statistics Probability 1 pp 197– (1956) [2] DOI: 10.2307/1267351 · Zbl 0202.17205 · doi:10.2307/1267351 [3] DOI: 10.1080/03610929308831027 · Zbl 0784.62065 · doi:10.1080/03610929308831027 [4] Rao C. R., Linear Models and Generalizations: Least Squares and Alternatives (2008) [5] DOI: 10.2307/2281073 · Zbl 0052.15503 · doi:10.2307/2281073 [6] DOI: 10.2307/2525589 · doi:10.2307/2525589 [7] DOI: 10.2307/2283275 · Zbl 0129.11401 · doi:10.2307/2283275 [8] Schaffrin B., Zeitschrift fur Angewandte Mathematik und Mechanik 70 pp 735– (1990) [9] DOI: 10.1080/03610929208830893 · Zbl 0774.62074 · doi:10.1080/03610929208830893 [10] DOI: 10.1080/03610929808832655 · Zbl 0960.62068 · doi:10.1080/03610929808832655 [11] DOI: 10.1080/03610927608827423 · Zbl 0342.62035 · doi:10.1080/03610927608827423 [12] DOI: 10.1016/j.spl.2003.07.005 · Zbl 1116.62368 · doi:10.1016/j.spl.2003.07.005 [13] Li Y. L., Stat. Pap. (2008) [14] Farebrother R. W., J. R. Stat. Soc. B 38 pp 248– (1976) [15] DOI: 10.1007/BF02924687 · Zbl 0703.62066 · doi:10.1007/BF02924687 [16] DOI: 10.1021/ie50275a002 · doi:10.1021/ie50275a002 [17] Kaciranlar S., Sankhya: Indian J. Stat. 61 pp 443– (1999) [18] DOI: 10.1080/03610920601144095 · Zbl 1124.62041 · doi:10.1080/03610920601144095 [19] DOI: 10.1081/SAC-120017499 · Zbl 1075.62588 · doi:10.1081/SAC-120017499 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.