Laboratory of Structural Methods of Data Analysis in Predictive
Modeling Moscow Institute of Physics and Technology
ENG
Логин:
Пароль:
Critical Dimension in the Semiparametric Bernstein von Mises Theorem
The classical parametric and semiparametric Bernstein–von Mises (BvM) results are reconsidered in a nonclassical setup allowing finite samples and model misspecification. In the parametric case and in the case of a finite-dimensional nuisance parameter, we establish an
upper bound on the error of Gaussian approximation of the posterior distribution of the target parameter; the bound depends explicitly on the dimension of the full and target parameters and on the sample size. This helps to identify the so-called critical dimension 'p_n' of the full parameter for which the BvM result is applicable. In the important special i.i.d. case, we show that the condition “p_n^3/n is small” is sufficient for the BvM result to be valid under general assumptions on the model. We also provide an example of a model with the phase transition effect: the statement of the BvM theorem fails when the dimension p_n approaches n^{1/3} .

Авторы: Panov Maxim , Spokoiny Vladimir

Дата: 29 декабря 2014

Статус: опубликована

Журнал: Proceedings of the Steklov Institute of Mathematics

Том: 287

Страницы: 232-255

Год: 2014

Google scholar:

Направления исследований

Statistical methods

Дополнительные материалы