Influence diagnostics in ridge semi parametric linear measurement error models

Document Type : Original Paper

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Abstract

In this paper influence diagnostics in the semi parametric linear measurement error is studied when the problem of multicollinearity is exist. First to combat multicollinearity, some ridge estimators are proposed based the penalized corrected likelihood approach, then using case deletion method the influence measures are defined to detect influential observations. In continue it is shown these measures are function of residuals and leverages. Furthrer more local influence approach is developed based the penalized likelihood function for assessing the influence of points. A simulation study is performed to illustrate the efficiency of proposed ridge estimators based on the asymptotically mean square error. Finally, the influence diagnostic approaches are applied to a real data.

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References

[1]  Cook,  R.  D.  (1977).  Detection  of  Influential  Observations  in  Linear  Regression. Technometrics, 19, 15-18. 
[2]  Cook,  R.  D.  and  Wesiberg,  S.  (1982).  Residuals and Influence in Regression. Chapman & Hall, New York  [3] Belsley, D. A., Kuh. E. and Welsch. R. E. (1980). Regression Diagnostics: Identifying Influential Data and Soureces of
Collinearity. John Wiley &  Sons, New York. 
[4] Kim, C. (1996). Cook’s Distance in Spline Smoothing, Statist Proba Lett.,  31, 139-144.  [5]  Kim,  C.,  Park,  B.  U.  and  Kim,  W.  (2002).  Influence  Diagnostics  in  Semiparametric Regression Models, Statist. Probab. Lett, 60, 49-58. 
 
Journal of Advanced Mathematical Modeling
Volume 8, Issue 1
September 2018
Pages 19-48

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History

  • Receive Date: 06 September 2016
  • Revise Date: 02 June 2018
  • Accept Date: 13 August 2018

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