Capturing Nonconformity Points in Regression

by James E. Mays .

Abstract: Of interest is obtaining an adequate fit to regression data when there is both a small sample size and a possible misspecification of the form of the underlying model. Confidence intervals are developed (using hat matrices from a linear model) for two semiparametric model-robust regression techniques, and these are compared to intervals from the individual parametric and nonparametric methods of ordinary least squares (OLS) and local linear regression (LLR). Special interest is given to comparisons at specific data points that do not conform to the chosen underlying model. The model-robust techniques perform as well as OLS even when there is no misspecification present in the chosen model, and as well or better than LLR when there is large misspecification. These benefits are apparent for optimal theoretical fits and for fits based on recently developed data-driven criteria.

Key Words: Regression, Robust, Misspecification, Semipar

James E. Mays,

Editor: Jeffrey S. Simonoff ,

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