On shrinkage estimators improving the positive part of James-Stein estimator

• Autorzy: Hamdaoui Abdenour

Identyfikatory

DOI

10.1515/dema-2021-0038

• Języki publikacji: EN

Abstrakty

EN

In this work, we study the estimation of the multivariate normal mean by different classes of shrinkage estimators. The risk associated with the quadratic loss function is used to compare two estimators. We start by considering a class of estimators that dominate the positive part of James-Stein estimator. Then, we treat estimators of polynomial form and prove if we increase the degree of the polynomial we can build a better estimator from the one previously constructed. Furthermore, we discuss the minimaxity property of the considered estimators.

Słowa kluczowe

EN

James-Stein estimator; multivariate normal distribution; non-central chi-square distribution; quadratic loss function; shrinkage estimators

PL

estymator; estymator Stein'a; rozkład normalny; rozkład chi-kwadrat; estymatory skurczu

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 462--473
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Hamdaoui Abdenour

• Department of Mathematics, University of Sciences and Technology, Mohamed Boudiaf, Oran, Laboratory of Statistics and Random Modelisations of Tlemcen University (LSMA), Algeria

Bibliografia

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• [12] A. Benkhaled and A. Hamdaoui, General classes of shrinkage estimators for the multivariate normal mean with unknown variance: Minimaxity and limit of risks ratios, Kragujevac J. Math. 46 (2019), no. 2, 193–213.
• [13] A. Hamdaoui, A. Benkhaled, and M. Mezouar, Minimaxity and limits of risks ratios of shrinkage estimators of a multivariate normal mean in the Bayesian case, Stat. Optim. Inf. Comput. 8 (2020), no. 2, 507–520, DOI: https://doi.org/10.19139/soic-2310-5070-735.
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• [15] S. Kaciranlar and I. Dawoud, The optimal extended balanced loss function estimators, J. Comput. Appl. Math. 345 (2019), 86–98, DOI: https://doi.org/10.1016/j.cam.2018.06.021.
• [16] W. James and C. Stein, Estimation with quadratic loss, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, University of California Press, Berkeley, 1961, pp. 361–379.
• [17] G. Casella and J. T. Hwang, Limit expressions for the risk of James-Stein estimators, Canad. J. Statist. 4 (1982), 305–309.
• [18] P. Y.-S. Shao and W. E. Strawderman, Improving on the James-Stein positive part estimator, Ann. Statist. 22 (1994), no. 3, 1517–1538, DOI: https://doi.org/10.1214/aos/1176325640.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).