Lo, Albert Y.; Sazonov, V. V. On normal approximation of large products of functions: A refinement of Blackwell’s result. (English) Zbl 1005.62013 Georgian Math. J. 8, No. 2, 319-322 (2001). From the paper: D. Blackwell [Approximate normality of large products. Tech. Rep. No. 54, Dpt. Stat., Univ. California, Berkeley (1995)], using a simple elementary way, proved that under some conditions standardized products of large numbers of smooth positive functions are close to \(\exp(-x^2/2)\). Moreover, he gave an estimation of this closeness. In the present note we observe that, under additional smoothness conditions, a little more effort provides an asymptotic expansion making this closeness still more precise. This result is closely related to the Bernstein-von Mises theorem on the normal approximation of posterior distributions. MSC: 62E20 Asymptotic distribution theory in statistics 62F15 Bayesian inference 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) Keywords:approximation of large products of functions; Bernstein-von Mises theorem PDFBibTeX XMLCite \textit{A. Y. Lo} and \textit{V. V. Sazonov}, Georgian Math. J. 8, No. 2, 319--322 (2001; Zbl 1005.62013) Full Text: EuDML