On local moments

JOURNAL OF MULTIVARIATE ANALYSIS

卷:76

Article

Müller, HG ; Yan, X

关键词: contour;    density estimation;    dependence function;    derivative estimation;    local covariance;    local geometry;    local mean;    mode estimation;    multivariate data analysis;   

DOI  :  10.1006/jmva.2000.1921

来源: Elsevier

【 摘 要 】

We introduce the concept of local moments for a distribution in R-p, p greater than or equal to 1, at a point z is an element of R-p. Local moments are defined as normalized limits: of the ordinary moments of a truncated version of the distribution. ignoring the probability mass falling. outside a window centered at z. The limit is obtained as the size of the window converges to 0. Corresponding local sample moments are obtained via properly normalized ordinary sample moments calculated from those data falling into a small window. The must prominent local sample moments are the local sample mean which is simply the standardized mean vector of the data falling into the window, and the local covariance, which is a standardized version of the covariance matrix of the data in the window. We establish consistency with rates of convergence and asymptotic distributions for local sample moments as estimates of the local moments. First and second order local moments are of particular interest and some applications are outlined. These include locally based iterative estimation of modes and contours and the estimation of the strength of local association. (C) 2001 Academic Press.

【 授权许可】

Free