Abstract
When a real-world data set is fitted to a specific type of models, it is often encountered that one or a set of observations have undue influence on the model fitting, which may lead to misleading conclusions. Therefore, it is necessary for data analysts to identify these influential observations and assess their impact on various aspects of model fitting. In this paper, one type of modified Cook’s distances is defined to gauge the influence of one or a set observations on the estimate of the constant coefficient part in partially varyingcoefficient models, and the Cook’s distances are expressed as functions of the corresponding residuals and leverages. Meanwhile, a bootstrap procedure is suggested to derive the reference values for the proposed Cook’s distances. Some simulations are conducted, and a real-world data set is further analyzed to examine the performance of the proposed method. The experimental results are satisfactory.
Similar content being viewed by others
References
Atkinson, A.C. Two graphical displays for outlying and influential observations in regression. Biometrika, 68(1):13–20 (1981)
Banerjee, M., Frees, E.W. Influence diagnostics for linear longitudinal models. J. Amer. Statist. Assoc., 92(439):999–1005 (1997)
Belsley, D.A. Kuh, E., Welsch, R.E. Regression diagnostics:identifying influential data and sources of collinearity. Wiley, New York, 1980
Cook, R.D. Detection of influential observations in linear regression. Techometrics, 19(1):15–18 (1977)
Cook, R.D., Weisberg, S. Residuals and influence in regression. Chapman and Hall, New York, 1982
Fan, J., Huang, T. Profile likelihood inferences on semiparametric varying-coefficient partially linear models. Bernoulli, 11(6):1031–1057 (2005)
Hastie, T.J., Tibshirani, R.J. Generalized additive models. Chapman and Hall, London, 1990
Hastie, T.J., Tibshirani, R.J. Varying-coefficient models (with discussion). J. R. Statist. Soc. B, 55(4):757–796 (1993)
Hart, J.D. Nonparametric smoothing and lack-of-fit tests. Springer-Verlag, New York, 1997
Kim, C. Cook’s distance in spline smoothing. Statist. Probab. Lett., 31(2):139–144 (1996)
Kim, C., Kim, W. Some diagnostics results in nonparametric density estimation. Comm. Statist. Theory Methods, 27:291–303 (1998)
Kim, C., Lee, Y., Park, B.U. Cook’s distance in local polynomial regression. Statist. Probab. Lett., 54(1):33–40 (2001)
Kim, C., Park, B.U., Kim, W. Influence diagnostics in semiparametric regression models. Statist. Probab. Lett., 60(1):49–58 (2002)
Kim, C., Storer, B.E. Reference values for Cook’s distance. Comm. Statist. Simulation Comput., 25:691–709 (1996)
Zhang, W.Y., Lee, S.Y., Song, X.Y. Local polynomial fitting in semivarying coefficient models. J. Multivar. Anal., 82(1):166–188 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundations of China (No. 10531030, No. 60675013).
Rights and permissions
About this article
Cite this article
Zhang, Cx., Mei, Cl. & Zhang, Js. Influence Diagnostics in Partially Varying-Coefficient Models. Acta Mathematicae Applicatae Sinica, English Series 23, 619–628 (2007). https://doi.org/10.1007/s10255-007-0400
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10255-007-0400