On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach

Ahmad

doi:https://doi.org/10.54216/NIF.030104

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Volume 3 • Issue 1 • PP: 27-33 • 2024

On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach

Ahmad Khaldi ^1*

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¹Mutah University, Faculty of Science, Jordan

* Corresponding Author.

DOI https://doi.org/10.54216/NIF.030104

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Received: May 02, 2023 Accepted: January 13, 2024

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Abstract

In this paper, we study the problem of estimating variance components in the two-way classification with interaction in the random effect linear model by non-linear maximization. We assume the model according to the assumptions and give the theory of derivation of the estimators of these components, then apply these estimators on real data and obtain the estimates. We estimate these components by two other methods: the solution of the expected equation of mean square in the analysis of the variance table, and the minimum variance quadratic unbiased estimator.

Keywords

Variance Linear model Non-linear maximization Estimation theory

References

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[5] Mardia, K. V. and Marshall, R. J. (1984), Maximum likelihood Estimation of Models for Residual Covariance In Spatial Regression Biometrika, 73, 135-146.

[6] Rao, C. R. and kleffe, J. (1988) : Estimation of variance component and application north Holland, Amsterdam

[7] Searle, S. R. (1988). Lecture notes on Variance Component. Biometrics unit, Cornell University, Ithaca, New York.

[8] Searle, S. R. Casella, G. and Mc culloch, C. E. (1992): Variance Component. Wiley, New York.

[9] ASHISH, DAS, Himadri Ghosn (2003): Estimation of Ratio of Variance Component and Optimal Dialed Cross Designs. http: // www.isid.ac.in / ~ statmath / eprints Indian statistical institute, Delhi centre 7.

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Khaldi, Ahmad. "On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach." Neutrosophic and Information Fusion, vol. Volume 3, no. Issue 1, 2024, pp. 27-33. DOI: https://doi.org/10.54216/NIF.030104

Khaldi, A. (2024). On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach. Neutrosophic and Information Fusion, Volume 3(Issue 1), 27-33. DOI: https://doi.org/10.54216/NIF.030104

Khaldi, Ahmad. "On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach." Neutrosophic and Information Fusion Volume 3, no. Issue 1 (2024): 27-33. DOI: https://doi.org/10.54216/NIF.030104

Khaldi, A. (2024) 'On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach', Neutrosophic and Information Fusion, Volume 3(Issue 1), pp. 27-33. DOI: https://doi.org/10.54216/NIF.030104

Khaldi A. On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach. Neutrosophic and Information Fusion. 2024;Volume 3(Issue 1):27-33. DOI: https://doi.org/10.54216/NIF.030104

A. Khaldi, "On The Problem of the Estimation of Variance Components Based On Non-linear Maximization Approach," Neutrosophic and Information Fusion, vol. Volume 3, no. Issue 1, pp. 27-33, 2024. DOI: https://doi.org/10.54216/NIF.030104

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