A technique is applied to estimate the parameters of the bivariate normal distribution with unknown mean vector and unknown covariance matrix by minimizing the Cramer von Mises distance from a non-parametric density estimate and the parametric estimate at the order statistics. The maximum likelihood estimators were found and a comparison was made with the proposed estimator. For different parameters of the true density the proposed estimators were tested using a Monte Carlo experiment. The results show an improvement in mean integrated square error which is taken as a measure of the closeness of the estimated density and the true density.
Sultan, A., Moore, A., & Khaleel, H. (2001). On Estimating the Parameters of the Bivariate Normal Distribution. The Egyptian Statistical Journal, 45(2), 143-154. doi: 10.21608/esju.2001.313810
MLA
Ahmed M.M. Sultan; Albert H. Moore; Hala Mohamed Khaleel. "On Estimating the Parameters of the Bivariate Normal Distribution", The Egyptian Statistical Journal, 45, 2, 2001, 143-154. doi: 10.21608/esju.2001.313810
HARVARD
Sultan, A., Moore, A., Khaleel, H. (2001). 'On Estimating the Parameters of the Bivariate Normal Distribution', The Egyptian Statistical Journal, 45(2), pp. 143-154. doi: 10.21608/esju.2001.313810
VANCOUVER
Sultan, A., Moore, A., Khaleel, H. On Estimating the Parameters of the Bivariate Normal Distribution. The Egyptian Statistical Journal, 2001; 45(2): 143-154. doi: 10.21608/esju.2001.313810
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