Diagnostics and Robust Estimation When Transforming the Regression Model and the Response

摘要

In regression analysis, the response is often transformed to remove heteroscedasticity and/or skewness. When a model already exists for the untransformed response, then it can be preserved by applying the same transform to both the model and the response. This methodology, which is called transform both sides, has been applied in several recent papers and appears highly useful in practice. When a parametric transformation family such as the power transformations is used, then the transformation can be estimated by maximum likelihood. The maximum likelihood estimator, however, is very sensitive to outliers. This article proposes diagnostics to indicate cases influential for the transformation or regression parameters. Also proposed is a robust bounded-influence estimator similar to the Krasker-Welsch regression estimator. Keywords: Reprints; Nonlinear models; Covariance matrix; Fisheries analysis.