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Restricted Distance-Type Gaussian Estimators Based on Density Power Divergence and Their Applications in Hypothesis Testing

Author

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  • Ángel Felipe

    (Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain)

  • María Jaenada

    (Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain)

  • Pedro Miranda

    (Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain)

  • Leandro Pardo

    (Department of Statistics and Operational Research, Complutense University of Madrid, 28040 Madrid, Spain)

Abstract

In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a simple null hypothesis, and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study.

Suggested Citation

  • Ángel Felipe & María Jaenada & Pedro Miranda & Leandro Pardo, 2023. "Restricted Distance-Type Gaussian Estimators Based on Density Power Divergence and Their Applications in Hypothesis Testing," Mathematics, MDPI, vol. 11(6), pages 1-41, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1480-:d:1100666
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    References listed on IDEAS

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    1. Castilla, Elena & Zografos, Konstantinos, 2022. "On distance-type Gaussian estimation," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Basu, Ayanendranath & Chakraborty, Soumya & Ghosh, Abhik & Pardo, Leandro, 2022. "Robust density power divergence based tests in multivariate analysis: A comparative overview of different approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Menendez, M. & Morales, D. & Pardo, L. & Vajda, I., 1995. "Divergence-Based Estimation and Testing of Statistical Models of Classification," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 329-354, August.
    4. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    5. A. Basu & A. Mandal & N. Martin & L. Pardo, 2018. "Testing Composite Hypothesis Based on the Density Power Divergence," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 222-262, November.
    6. F. Götze & A. Tikhomirov, 2002. "Asymptotic Distribution of Quadratic Forms and Applications," Journal of Theoretical Probability, Springer, vol. 15(2), pages 423-475, April.
    7. Ayanendranath Basu & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2022. "A Robust Generalization of the Rao Test," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 868-879, April.
    8. Wu, Wei Biao & Shao, Xiaofeng, 2007. "A Limit Theorem For Quadratic Forms And Its Applications," Econometric Theory, Cambridge University Press, vol. 23(5), pages 930-951, October.
    9. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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