1MODEL-ROBUST CONFIDENCE INTERVALS AND CAPTURING NONCONFORMITY POINTS

The variability and accuracy of two recently published semiparametric model-robust regression techniques are studied through the development and assessment of confidence intervals. The specific problem addressed is obtaining an adequate fit to data when there is both a small sample size and a possible misspecification of the form of the underlying model. Classical parametric procedures such as ordinary least squares (OLS) would result in inaccurate fits, at least in the portions of the data that do not conform to the chosen underlying model. Unfortunately, the nonparametric alternatives, such as local linear regression (LLR), have been shown to possess high variance problems in the small-sample scenario. This would lead to undesirably wide confidence intervals. The solution to this dilemma is to use a semiparametric model-robust technique that combines the useful parametric information available with a nonparametric adjustment to capture the structure missed by the parametric fit. Confidence intervals for two of these methods are developed (using hat matrices from a linear model) and compared to those from OLS and LLR. Several examples and a simulation study establish the benefits of the model-robust intervals by comparing coverage probabilities and median widths. These benefits are apparent for optimal theoretical fits and for fits based on recently developed data-driven criteria. 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. Most importantly, the model-robust techniques significantly outperform both the OLS and LLR techniques when there is small misspecification present, and make it possible to take advantage of the benefits of using nonparametric techniques in a small-sample problem