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.