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**Robust Bayesian estimators in a one-way ANOVA model.**
*(English)*
Zbl 0839.62024

Summary: Motivated by the attractive features of robust priors, we develop Bayesian estimators for the parameters in a one-way ANOVA model using mixed priors, which are formed by incorporating a \(t\) density into the usual conjugate priors to independently describe prior knowledge regarding the overall mean or regarding the factor effects. The effect of the independent \(t\) prior component is greatly different from that of the conjugate prior. The Bayesian estimators arising from such mixed priors are nonlinear functions of the least squares estimators and adjust automatically to the value of the sum of squared errors. In this sense, they are adaptive and rather insensitive to extreme observations. The proposed estimators are clearly superior to the usual Bayesian estimators and to the traditional unbiased estimators, and may be practicable when the error terms are Cauchy distributed.

### MSC:

62F15 | Bayesian inference |

62J10 | Analysis of variance and covariance (ANOVA) |

62F35 | Robustness and adaptive procedures (parametric inference) |

### Keywords:

\(t\) density; Behrens-Fisher density; poly-Cauchy density; poly-\(t\) density; posterior mean; posterior mode; robust priors; Bayesian estimators; one-way ANOVA model; mixed priors; conjugate priors; nonlinear functions of the least squares estimators; sum of squared errors### References:

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