Nonasymptotic approach to Bayesian semiparametric inference
- Авторлар: Panov M.1,2,3
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Мекемелер:
- Institute for Information Transmission Problems
- Moscow Institute of Physics and Technology
- Datadvance Company
- Шығарылым: Том 93, № 2 (2016)
- Беттер: 155-158
- Бөлім: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223469
- DOI: https://doi.org/10.1134/S1064562416020101
- ID: 223469
Дәйексөз келтіру
Аннотация
The classical semiparametric Bernstein–von Mises (BvM) results is reconsidered in a non-classical setup allowing finite samples and model misspecication. We obtain an upper bound on the error of Gaussian approximation of the posterior distribution for the target parameter which is explicit in the dimension of the target parameter and in the dimension of sieve approximation of the nuisance parameter. This helps to identify the so called critical dimension pn of the sieve approximation of the full parameter for which the BvM result is applicable. If the bias induced by sieve approximation is small and dimension of sieve approximation is smaller then critical dimension than the BvM result is valid. In the important i.i.d. and regression cases, we show that the condition “pn2q/n is small”, where q is the dimension of the target parameter and n is the sample size, leads to the BvM result under general assumptions on the model.
Авторлар туралы
M. Panov
Institute for Information Transmission Problems; Moscow Institute of Physics and Technology; Datadvance Company
Хат алмасуға жауапты Автор.
Email: panov.maxim@gmail.com
Ресей, Bol’shoi Karetnyi per. 19/1, Moscow, 127994; Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700; Moscow