| 讲座简介： | The Gaussian distribution, univariate and multivariate, has a unique place in statistics. For instance, for a Gaussian distribution dependence is completely determined by correlation between pairs of variables. The idea of local Gaussian approximation is to approximate a bivariate (multivariate) density locally by a bivariate (multivariate) Gaussian density. The correlation function of the approximating Gaussian is taken as the local Gaussian correlation at this location. It is a very useful nonlinear dependence measure. In the talk I will review some recent developments, including the local Gaussian autocorrelation and its use in measuring nonlinear serial dependence in time series. Moreover, I will cover semiparametric multivariate density estimation with increasing dimension, conditional density estimation, local partial correlation and perspectives emanating from this. Illustrations will be given from recent publications and preprints. |
