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ON STATISTICAL MODELS FOR REGRESSION DIAGNOSTICS

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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.

**Source**
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