Laboratory of Structural Methods of Data Analysis in Predictive
Modeling Moscow Institute of Physics and Technology
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