A note on a posterior approximation in a heteroscedastic model. (English) Zbl 1273.62165
Summary: We develop a method of obtaining approximate marginal posteriors for all parameters of interest for a heteroscedastic model. This method improves upon G. E. P. Box and W. J. Hill’s method [Technometrics 16, 385–389 (1974; Zbl 0283.62063)] in suggesting a pure Bayesian estimator for a regression coefficient.
MSC:
| 62J05 | Linear regression; mixed models |
| 62P20 | Applications of statistics to economics |
| 62F15 | Bayesian inference |
Citations:
Zbl 0283.62063References:
| [1] | Box, G. E.P.; Hill, W. J., Correcting inhomogeneity of variance with power transformation weighting, Technometrics, 16, 385-389 (1974) · Zbl 0283.62063 |
| [2] | Johnson, R. A., Asymptotic expansions for posterior distributions, The Annals of Mathematical Statistics, 41, 851-864 (1970) · Zbl 0204.53002 |
| [3] | Kloek, T.; Van Dijk, H. K., Bayesian estimates of equation system parameters: An application of integration by Monte Carlo, Econometrica, 46, 1-19 (1978) · Zbl 0376.62014 |
| [4] | Zellner, A., An introduction to Bayesian inference in econometrics (1971), Wiley: Wiley New York · Zbl 0246.62098 |
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