Estimation after selection from bivariate normal population using LINEX loss function
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866916371954139136 |
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| author | Arshad, Mohd. Abdalghani, Omer Meena, Kalu Ram |
| author_facet | Arshad, Mohd. Abdalghani, Omer Meena, Kalu Ram |
| contents | Let $π_1$ and $π_2$ be two independent populations, where the population $π_i$ follows a bivariate normal distribution with unknown mean vector $\boldsymbolθ^{(i)}$ and common known variance-covariance matrix $Σ$, $i=1,2$. The present paper is focused on estimating a characteristic $θ_{\textnormal{y}}^S$ of the selected bivariate normal population, using a LINEX loss function. A natural selection rule is used for achieving the aim of selecting the best bivariate normal population. Some natural-type estimators and Bayes estimator (using a conjugate prior) of $θ_{\textnormal{y}}^S$ are presented. An admissible subclass of equivariant estimators, using the LINEX loss function, is obtained. Further, a sufficient condition for improving the competing estimators of $θ_{\textnormal{y}}^S$ is derived. Using this sufficient condition, several estimators improving upon the proposed natural estimators are obtained. Further, a real data example is provided for illustration purpose. Finally, a comparative study on the competing estimators of $θ_{\text{y}}^S$ is carried-out using simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_05422 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Estimation after selection from bivariate normal population using LINEX loss function Arshad, Mohd. Abdalghani, Omer Meena, Kalu Ram Statistics Theory Let $π_1$ and $π_2$ be two independent populations, where the population $π_i$ follows a bivariate normal distribution with unknown mean vector $\boldsymbolθ^{(i)}$ and common known variance-covariance matrix $Σ$, $i=1,2$. The present paper is focused on estimating a characteristic $θ_{\textnormal{y}}^S$ of the selected bivariate normal population, using a LINEX loss function. A natural selection rule is used for achieving the aim of selecting the best bivariate normal population. Some natural-type estimators and Bayes estimator (using a conjugate prior) of $θ_{\textnormal{y}}^S$ are presented. An admissible subclass of equivariant estimators, using the LINEX loss function, is obtained. Further, a sufficient condition for improving the competing estimators of $θ_{\textnormal{y}}^S$ is derived. Using this sufficient condition, several estimators improving upon the proposed natural estimators are obtained. Further, a real data example is provided for illustration purpose. Finally, a comparative study on the competing estimators of $θ_{\text{y}}^S$ is carried-out using simulation. |
| title | Estimation after selection from bivariate normal population using LINEX loss function |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/1911.05422 |