A REVIEW OF THE DEVELOPMENT AND APPLICATION OF RECURSIVE RESIDUALS INLINEAR-MODELS

Recursive residuals have been shown to be useful in a variety of appli cations in linear models. Unlike the more familiar ordinary least squa res residuals or studentized residuals, recursive residuals are indepe ndent as well as homoscedastic under the model. Their independence is particularly appealing for use in developing test statistics. They are not uniquely defined; their values depend on the order in which they are calculated, although their properties do not. In some applications one can exploit this order dependence, coupled with the fact that the y are in clear one-to-one correspondence with the observations for whi ch they are calculated. Uses for recursive residuals have been suggest ed in almost all areas of regression model validation. Regression diag nostics have been constructed from recursive residuals for detecting s erial correlation, heteroscedasticity, functional misspecification, an d structural change. Other statistics based on recursive residuals hav e focused on detection of outliers or observations that are influentia l or have high leverage. Recent work has explored properties and possi ble uses of recursive residuals in models with a general covariance ma trix, multivariate linear models, and nonlinear models. Computing rout ines are available for obtaining recursive residuals accurately and ef ficiently.