Heteroscedastic Regression Models and Applications to Off‐line Quality Control

We discuss in the present paper the analysis of heteroscedastic regression models and their applications to off‐line quality control problems. It is well known that the method of pseudo‐likelihood is usually preferred to full maximum likelihood since estimators of the parameters in the regression function obtained are more robust to misspecification of the variance function. Despite its popularity, however, existing theoretical results are difficult to apply and are of limited use in many applications. Using more recent results in estimating equations, we obtain an efficient algorithm for computing the pseudo‐likelihood estimator with desirable convergence properties and also derive simple, explicit and easy to apply asymptotic results. These results are used to look in detail at variance minimization in off‐line quality control, yielding techniques of inferences for the optimized design parameter. In application of some existing approaches to off‐line quality control, such as the dual response methodology, rigorous statistical inference techniques are scarce and difficult to obtain. An example of off‐line quality control is presented to discuss the practical aspects involved in the application of the results obtained and to address issues such as data transformation, model building and the optimization of design parameters. The analysis shows very encouraging results, and is seen to be able to unveil some important information not found in previous analyses.