In this study, robust estimators were applied to an RxC contingency table with an outlier to obtain the robust parameter estimates instead of the maximum likelihood (ML) estimates, and the results were discussed.
📌 3 Key Takeaways
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Objective & Hypothesis:If all cell counts $n_ij$ of a given R x C contingency table are positive, estimates of the expected frequencies mjj can be found by applying any regression estimator to the logarithm of the observed counts.
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Key Findings & Data:If an R x C table contains outlier(s), ordinary least squares estimates will be affected by the outlier(s).
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Conclusion & Impact:In this study, robust estimators were applied to an RxC contingency table with an outlier to obtain the robust parameter estimates instead of the maximum likelihood (ML) estimates, and the results were discussed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
If all cell counts $n_ij$ of a given R x C contingency table are positive, estimates of the expected frequencies mjj can be found by applying any regression estimator to the logarithm of the observed counts. If an R x C table contains outlier(s), ordinary least squares estimates will be affected by the outlier(s). Various authors have proposed several robust estimators sensitive to outliers. In this study, robust estimators were applied to an RxC contingency table with an outlier to obtain the robust parameter estimates instead of the maximum likelihood (ML) estimates, and the results were discussed.
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Cite This Article
AKTAŞ, S., ÇETİN, M. (2022). M-estimators of the uniform association model in RxC contingency tables. Hacettepe Journal of Mathematics and Statistics, Cilt: 31 - Sayı:, 83–88. https://ajindex.com/articles/530840
1] Agresti, A. Categorical Data Analysis, John-Wiley, New-York, 1990 [2] Backman, R. C. and Cook R. D. "Outliers", Technometrics 25, 119-149, 1983. [3] Çetin, M. and Aktaş, S. R X C Çapraz Çizelgelerinde $L_1$ kestiricisi, İstatistik Sempozyumu 2000,
Gazi University, Ankara, 2000. [4] Goodman, L. A. The analysis of cross -classified data: Independence, quasi- independence and interactions in contingency tables with or without missing entries, JASA 63, 1091-1131, 1968. [5] Huber, P. J. Robust regression: Asymptotics, conjectures and Monte Carlo, Ann. Stat. 1, 799-821, 1973. [6] Huber, P. J. Robust Statistics, John Wiley & Sons Inc., New York, 308p, 1881. [7] Hubert, M. The breakdown value of the $L_1$ estimator in contingency tables, Statistics & Probability Letters 33, 419-425, 1997. [8] Hoaglin, D. C., Mosteller F. and Tukey, J. W. Understanding robust and exploratory data analysis, John Wiley & Sons, Inc., New York, 1983. [9] Rousseeuw, P.J. Robust regression and outlier detection, John-Wiley, New- York, 1984. [10] Ryan, T. P. Modern Regression Methods, John-Wiley, [11] SIS, Statistical yearbook in Turkey, 1999. New-York, 1997.