JSM 2005 Online Program

Abstract #303962

This is the preliminary program for the 2005 Joint Statistical Meetings in Minneapolis, Minnesota. Currently included in this program is the "technical" program, schedule of invited, topic contributed, regular contributed and poster sessions; Continuing Education courses (August 7-10, 2005); and Committee and Business Meetings. This on-line program will be updated frequently to reflect the most current revisions.

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Activity Number:	358
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor:	IMS
Abstract - #303962
Title:	The Weak Convergence of Empirical Processes from Multivariate Normal Vectors for Goodness-of-fit Tests
Author(s):	Christopher Saunders*+ and Constance L. Wood
Companies:	University of Kentucky and University of Kentucky
Address:	2020 Armstrong Mill rd, Lexington, KY, 40515, United States
Keywords:	Goodness-of-Fit ; Empirical Processes ; Quantile Processes ; P-Donsker ; Asymptotics
Abstract:	Goodness-of-fit tests for the multivariate normal distribution are proposed based on dependent univariate data that arises with a data-suggested linear transformation, which projects the data vector onto the real line. Let Y_i be a sequence of independent k-variate normal random vectors and let c_0 be a fixed-linear transform from R^k to R. For a sequence of linear transforms c_n converging almost surely to c_0, the weak convergence of the empirical process of the standardized projections from c_n to a tight Gaussian process is established. This tight Gaussian process is the same limiting process as in the univariate normal case where the mean and standard deviation are estimated by the sample mean and sample standard deviation (Wood 1975). This Gaussian process determines the limiting null distribution of goodness-of-fit statistics applied to the empirical and quantile processes of the projections.

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