scholarly journals COVRATIO Statistic as a Discrimination Method for Multivariate Normal Distribution

2021 ◽  
Vol 50 (7) ◽  
pp. 2079-2084
Author(s):  
Norli Anida Abdullah ◽  
Afera Mohamad Apandi ◽  
Mohd Iqbal Shamsudheen ◽  
Yong Zulina Zubairi
Keyword(s):  
Normal Distribution ◽  
Covariance Matrix ◽  
Multivariate Normal Distribution ◽  
Discrimination Function ◽  
Multivariate Normal ◽  
Full Dataset ◽  
Linear Discrimination ◽  
Simulation Results ◽  
Better Than ◽  
Discrimination Method

The COVRATIO statistic has been used to identify the presence of outlier in data, which is based on deletion approach, where the determinant of covariance matrix for the full dataset excludes i-th row. This study proposes a novel discrimination method for the multivariate normal (MVN) distribution using the idea of COVRATIO statistic, denoted as . The linear discrimination function (LDF) for MVN distribution will be compared to the statistic. Simulation results showed that the as discrimination method performs better than the LDF with lower misclassification probabilities in all cases considered. The interest in the discrimination method arose in connection with the study of an application to discriminate the shape of the human maxillary dental arches, thus statistic may be considered as an alternative.

Estimators which are Uniformly Better than the James-Stein Estimator

1997 ◽  
Vol 47 (3-4) ◽  
pp. 167-180 ◽  
Author(s):  
Nabendu Pal ◽  
Jyh-Jiuan Lin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Mean Estimation ◽  
Stein Estimator ◽  
Mean Vector ◽  
Better Than

Assume i.i.d. observations are available from a p-dimensional multivariate normal distribution with an unknown mean vector μ and an unknown p .d. diaper- . sion matrix ∑. Here we address the problem of mean estimation in a decision theoretic setup. It is well known that the unbiased as well as the maximum likelihood estimator of μ is inadmissible when p ≤ 3 and is dominated by the famous James-Stein estimator (JSE). There are a few estimators which are better than the JSE reported in the literature, but in this paper we derive wide classes of estimators uniformly better than the JSE. We use some of these estimators for further risk study.

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