Multivariate normal approximation of the maximum likelihood estimator via the delta method

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.

Download Full-text

On the maximum likelihood estimator for a discrete multivariate crash frequencies model

Afrika Statistika ◽

10.16929/as/2020.2325.161 ◽

2020 ◽

Vol 15 (2) ◽

pp. 2335-2348

Author(s):

Issa Cherif Geraldo

Keyword(s):

Statistical Analysis ◽

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Road Safety ◽

Strong Consistency ◽

Delta Method ◽

Closed Form Expression ◽

Parameter Vector ◽

Form Expression ◽

Likelihood Estimator

In this paper, we study the maximum likelihood estimator (MLE) of the parameter vector of a discrete multivariate crash frequencies model used in the statistical analysis of the effectiveness of a road safety measure. We derive the closed-form expression of the MLE afterwards we prove its strong consistency and we obtain the exact variance of the components of the MLE except one component whose variance is approximated via the delta method.

Download Full-text

Bounds for the normal approximation of the maximum likelihood estimator fromm-dependent random variables

Statistics & Probability Letters ◽

10.1016/j.spl.2017.04.022 ◽

2017 ◽

Vol 129 ◽

pp. 171-181

Author(s):

Andreas Anastasiou

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Normal Approximation ◽

Random Variables ◽

Likelihood Estimator ◽

Dependent Random Variables

Download Full-text

Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-735 ◽

2020 ◽

Vol 8 (2) ◽

pp. 507-520

Author(s):

Abdenour Hamdaoui ◽

Abdelkader Benkhaled ◽

Nadia Mezouar

Keyword(s):

Maximum Likelihood ◽

Sample Size ◽

Maximum Likelihood Estimator ◽

Bayes Estimator ◽

Shrinkage Estimators ◽

Multivariate Normal ◽

Likelihood Estimator ◽

Unknown Variance ◽

Multivariate Normal Mean ◽

Normal Mean

In this article, we consider two forms of shrinkage estimators of a multivariate normal mean with unknown variance. We take the prior law as a normal multivariate distribution and we construct a Modified Bayes estimator and an Empirical Modified Bayes estimator. We are interested instudying the minimaxity and the behavior of risks ratios of these estimators to the maximum likelihood estimator, when the dimension of the parameters space and the sample size tend to infinity.

Download Full-text