Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem

In his paper [T2] Terras obtained a central limit theorem for rotation- invariant random variables on the space of n x n real positive definite (symmetric) matrices in the case n =

Since every separable Banach space is isometric to a linear subspace of a space C(S), our central limit theorem gives as a corollary a general central limit theorem for separable

In Section 7 we study the asymptotic coverage level of the confidence interval built in Section 5 through two different sets of simulations: we first simulate a

Proposition 5.1 of Section 5 (which is the main ingredient for proving Theorem 2.1), com- bined with a suitable martingale approximation, can also be used to derive upper bounds for

Keywords: Berry-Esseen bounds, Central Limit Theorem, non-homogeneous Markov chain, Hermite-Fourier decomposition, χ 2 -distance.. Mathematics Subject Classification (MSC2010):

The rate of convergence in Theorem 1.1 relies crucially on the fact that the inequality (E r ) incorporates the matching moments assumption through exponent r on the

In other words, no optimal rates of convergence in Wasserstein distance are available under moment assumptions, and they seem out of reach if based on current available

In particular given n the number of observations, the choice of N = n/2 Fourier coefficients to estimate the integrated volatility is optimal and in this case, the variance is the