We prove the large deviation principle (LDP) for posterior distributions arising from subfamilies of full exponential families, allowing misspecification of the model. Moreover, motivated by the so-called inverse Sanov Theorem (see eg Ganesh and O'Connell, 1999, Ganesh and O'Connell, 2000), we prove the LDP for the corresponding maximum likelihood estimator, and we study the relationship between rate functions.
An inverse Sanov theorem for exponential families / Macci, Claudio; Piccioni, Mauro. - In: JOURNAL OF STATISTICAL PLANNING AND INFERENCE. - ISSN 0378-3758. - 224:(2023), pp. 54-68. [10.1016/j.jspi.2022.10.003]
An inverse Sanov theorem for exponential families
Mauro Piccioni
2023
Abstract
We prove the large deviation principle (LDP) for posterior distributions arising from subfamilies of full exponential families, allowing misspecification of the model. Moreover, motivated by the so-called inverse Sanov Theorem (see eg Ganesh and O'Connell, 1999, Ganesh and O'Connell, 2000), we prove the LDP for the corresponding maximum likelihood estimator, and we study the relationship between rate functions.| File | Dimensione | Formato | |
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