INFLUENCE ANALYSIS FOR LINEAR MEASUREMENT ERROR MODELS

XU-PING ZHONG^{1}, BO-CHENG WEI^{1} AND WING-KAM FUNG^{2}

1Department of Mathematics, Southeast University, Nanjing, 210096, China 2Department of Statistics, University of Hong Kong, Hong Kong, China

(Received March 9, 1998; revised June 2, 1998)

Abstract. In this paper, we present a unified diagnostic method for linear measurement error models based upon the corrected likelihood of Nakamura (1990, Biometrika, 77, 127–137). Both global influence and local influence are discussed. The case-deletion model and mean-shift outlier model are considered, and they are shown to be approximately equivalent. Several diagnostic measures are derived and discussed. It is found that they can be written in terms of the residual and leverage measure. Some existing results are improved. Numerical example illustrates that our method is useful for diagnosing influential observations.

Key words and phrases: Corrected likelihood, diagnostics, global influence, local influence, measurement error models.

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