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On distance-type Gaussian estimation

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  • Castilla, Elena
  • Zografos, Konstantinos

Abstract

In this paper, we develop a new procedure for estimating the parameters of a model by combining Zhang’s (2019) recent Gaussian estimator and the minimum density power divergence estimators of Basu et al. (1998). The proposed estimator is called the Minimum Density Power Divergence Gaussian Estimator (MDPDGE). The consistency and asymptotic normality of the MDPDGE are proved. The MDPDGE is applied to some classical univariate distributions and it is also investigated for the family of elliptically contoured distributions. A numerical study illustrates the robustness of the proposed estimator.

Suggested Citation

  • Castilla, Elena & Zografos, Konstantinos, 2022. "On distance-type Gaussian estimation," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21001093
    DOI: 10.1016/j.jmva.2021.104831
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    References listed on IDEAS

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    1. Kelejian, Harry H. & Prucha, Ingmar R., 1985. "Independent or uncorrelated disturbances in linear regression : An illustration of the difference," Economics Letters, Elsevier, vol. 19(1), pages 35-38.
    2. E. Castilla & N. Martín & L. Pardo & K. Zografos, 2021. "Composite likelihood methods: Rao-type tests based on composite minimum density power divergence estimator," Statistical Papers, Springer, vol. 62(2), pages 1003-1041, April.
    3. T. S. Breusch & J. C. Robertson & A. H. Welsh, 1997. "The emperor's new clothes: a critique of the multivariate t regression model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(3), pages 269-286, November.
    4. Zografos, K., 1999. "On Maximum Entropy Characterization of Pearson's Type II and VII Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 67-75, October.
    5. Kotz, Samuel & Nadarajah, Saralees, 2001. "Some extremal type elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 171-182, September.
    6. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "New robust statistical procedures for the polytomous logistic regression models," Biometrics, The International Biometric Society, vol. 74(4), pages 1282-1291, December.
    7. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, November.
    8. Zhang, Tonglin, 2019. "General Gaussian estimation," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 234-247.
    9. Ayanendranath Basu & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 493-522, July.
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    Cited by:

    1. 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.

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