Abstract
In this paper we are concerned with the influence of the a-priori precision of θ on the HPD-regions for the linear regression model y = Xθ + ε. For fixed a-priori mean the set of a-posteriori means of θ has been examined in detail by Learner and Chamberlain (1976) and Polasek (1984). It has been shown that this set forms an ellipsoid, the so-called feasible ellipsoid.
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References
Chamberlain, G. and Learner, E. E., 1976, Matrix weighted averages and posterior bounds, Journal Roy. Statist. Soc. Ser. B 38, 73–84.
Polasek, W., 1984, Multivariate regression systems -and sensitivity analysis of two-dimensional data, in: Robustness of Bayesian analyses, J. B. Kadane, ed., North-Holland, Amsterdam.
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© 1987 Plenum Press, New York
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Pötzelberger, K. (1987). Hpd-Regions for the Linear Regression Model. In: Viertl, R. (eds) Probability and Bayesian Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1885-9_40
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DOI: https://doi.org/10.1007/978-1-4613-1885-9_40
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9050-6
Online ISBN: 978-1-4613-1885-9
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