article Open Access
Maximum likelihood estimation for multivariate normal with auxiliary information
International Journal of Statistics and Applied Mathematics · 2021 · Vol. 6(4) · pp. 83–85
Jianqi Yu✉(Guilin University of Technology)Shaoling Ding(Guilin University of Technology)Xiang Wang(Guilin University of Technology)
Abstract
Closed forms are obtained for the maximum likelihood estimators (MLE) of the mean vectors and the covariance matrix of a multivariate normal samples using known means of auxiliary variables. The likelihood function is decomposed as product of several independent normal and conditional normal likelihood functions. The parameters are transformed into a new set of parameters of which the MLEs are easy to derive. Since the MLE are invariant, the MLE of the original parameters are derived using the inverse transformation.MSC2000 subject classi cations: 62H12; 62H15.
Survey Sampling and Estimation TechniquesStatistical Methods and Bayesian InferenceAdvanced Statistical Methods and ModelsMathematicsMultivariate normal distributionLikelihood functionMatrix t-distributionStatisticsRestricted maximum likelihoodMultivariate statisticsEstimatorMaximum likelihoodScatter matrix
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