JSM 2004 - Toronto

Abstract #300619

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Activity Number: 232
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #300619
Title: Simulations for Robust Tests of Many Outliers in Regression
Author(s): Anthony C. Atkinson*+
Companies: London School of Economics
Address: Dept. of Statistics, London, International, WC2A 2AE, United Kingdom
Keywords: forward search ; simulation envelopes ; trimmed estimators
Abstract:

Tests of outliers in regression need estimates of both the parameters of the linear model and of the error variance. If the outliers are included in the set of observations used for estimation, inconsistent estimates of the parameters will be obtained and the existence and the effect of the outliers will be masked. We therefore consider procedures in which the observations are divided into two groups; the good observations are used to provide estimates of the parameters and the remainder are tested for outlyingness. We are interested in the null distribution of the outlier test. In the simplest case, that of location, we would base our estimates on the m central observations, trimming the remainder. The properties of our estimators would then be those coming from this trimmed sample of n observations. We use this insight, combined with the Forward Search, to provide three excellent approximations to the distribution of the outlier test in regression. The talk will emphasize robust data analysis.

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