Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 1, pp. 86--109

EXCHANGEABILITY, PREDICTIVE DISTRIBUTIONS AND PARAMETRIC MODELS

By

SANDRA FORTINI, Università ``L. Bocconi",
LUCIA LADELLI,Politecnico di Milano,

and

EUGENIO REGAZZINI, Università di Pavia, CNR-IAMI.

SUMMARY. In the general setting of predictive inference, when observations are exchangeable and take values in a Polish space, conditions are stated in order that parametric models turn out to be limiting forms of predictive distributions and parameters are limiting forms of suitable predictive sufficient statistics. The treatment is completed by a necessary and sufficient condition in order that a sequence of predictive distributions may be consistent with an exchangeable distribution. Moreover, main properties of predictive sufficiency are revisited in the general setting described above.

AMS (1991) subject classification. Primary: 62A15. secondary: 60G09, 62B20.

Key words and phrases. de Finetti's measure, exchangeable random variables, exponential model, predictive distributions, predictive sufficient statistics.

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