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Statistica Sinica 9(1999), 571-594


Hans-Georg Müller and Peng-Liang Zhao

University of California, Davis and Merck Research Laboratories

Abstract: We introduce Domain Splitting as a new tool for regression analysis. This device corresponds to splitting the domain of a regression function into m subdomains, where m is varied, and fitting a linear model on each subdomain. The residual sums of squares from these various fits are compared graphically. Domain Splitting provides a visual diagnostic, as well as a model-independent estimate of the error variance. We investigate the asymptotic behavior of Domain Splitting for the cases of an underlying linear model and that of a smooth regression function. The asymptotic findings are illustrated in simulations and examples.

Key words and phrases: Diagnostic plot, goodness-of-fit, linear model, model selection, smooth regression, variance estimation.

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