ON STATISTICAL MODELS FOR REGRESSION DIAGNOSTICS

BO-CHENG WEI AND JIAN-QING SHIH

Department of Mathematics, Southeast University, Si Pai Lou^{∗2}, Nanjing 210018, China

(Received August 24, 1992; revised March 31, 1993)

Abstract. In regression diagnostics, the case deletion model (CDM) and the mean shift outlier model (MSOM) are commonly used in practice. In this paper we show that the estimates of CDM and MSOM are equal in a wide class of statistical models, which include LSE, MLE, Bayesian estimate and M-estimate in linear and nonlinear regression models; MLE in generalized linear models and exponential family nonlinear models; MLEs of transformation parameters of explanatory variables in a Box-Cox regression models and so on. Furthermore, we study some models, in which, the estimates are not exactly equal but are approximately equal for CDM and MSOM.

Key words and phrases: Case deletion model, exponential family nonlinear models, mean-shift outlier model, nonlinear regression models, regression transformation, proportional hazards models.