Bernstein-von Mises Theorems for Functionals of Covariance

Parameter Estimation of Some Archimedean Copulas Based on Minimum Cramér-von-Mises Distance

The purpose of this paper is to introduce a new estimation method for estimating the Archimedean copula dependence parameter in the non-parametric setting. The estimation of the dependence parameter has been selected as the value that minimizes the Cramér-von-Mises distance which measures the distance between Empirical Bernstein Kendall distribution function and true Kendall distribution functi...

Bernstein von Mises Theorems for Gaussian Regression with increasing number of regressors

Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications

A numerical approximation of the critical values of Cramér-von Mises (CvM) tests is proposed for testing the correct specification of general conditional location parametric functionals. These specifications include conditional mean and quantile models. The method is based on the estimation of the eigenelements of the covariance operator associated with the CvM test, and it has the advantage th...

A semiparametric Bernstein - von Mises theorem for Gaussian process priors

This paper is a contribution to the Bayesian theory of semiparametric estimation. We are interested in the so-called Bernstein-von Mises theorem, in a semiparametric framework where the unknown quantity is (θ , f ), with θ the parameter of interest and f an infinite-dimensional nuisance parameter. Two theorems are established, one in the case with no loss of information and one in the informati...

The Bernstein-von Mises Theorem for Stationary Processes

In the literature of time series analysis since Whittle (1953), many authors (for example, Dunsmuir and Hannan (1976), Dunsmuir (1979), and Hosoya and Taniguchi (1982)) have considered an approach using Whittle’s log-likelihood, which is an approximation of Gaussian log-likelihood of the data, and have developed the asymptotic properties of an estimator that maximizes Whittle’s loglikelihood. T...