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Influence diagnostics in semiparametric regression models

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  • Kim, Choongrak
  • Park, Byeong U.
  • Kim, Woochul

Abstract

In this paper we consider the semiparametric regression model, Y=x'[beta]+m(t)+[var epsilon], and provide some influence diagnostics for estimators of [beta], m and the mean response x'[beta]+m(t). We express these influence diagnostics as functions of the residuals and leverages. We find that an influential observation on the estimator of the coefficient vector [beta] may not be influential on that of the nonparametric component m, and vice versa. Also, an observation which is not influential on each of them may be influential on the estimator of the mean response. Therefore, influence of an observation should be evaluated on each estimator separately. An illustrative example based on a real data set is also given.

Suggested Citation

  • Kim, Choongrak & Park, Byeong U. & Kim, Woochul, 2002. "Influence diagnostics in semiparametric regression models," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 49-58, November.
    • Handle: RePEc:eee:stapro:v:60:y:2002:i:1:p:49-58
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    References listed on IDEAS

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    1. Kim, Choongrak & Lee, Yonjoo & Park, Byeong U., 2001. "Cook's distance in local polynomial regression," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 33-40, August.
    2. Kim, Choongrak, 1996. "Cook's distance in spline smoothing," Statistics & Probability Letters, Elsevier, vol. 31(2), pages 139-144, December.
    3. Wing‐Kam Fung & Zhong‐Yi Zhu & Bo‐Cheng Wei & Xuming He, 2002. "Influence diagnostics and outlier tests for semiparametric mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 565-579, August.
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    Cited by:

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    2. Li, Zaixing & Xu, Wangli & Zhu, Lixing, 2009. "Influence diagnostics and outlier tests for varying coefficient mixed models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2002-2017, October.
    3. Emami, Hadi, 2015. "Influence diagnostic in ridge semiparametric models," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 106-113.
    4. Manghi, Roberto F. & Cysneiros, Francisco José A. & Paula, Gilberto A., 2019. "Generalized additive partial linear models for analyzing correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 47-60.
    5. Germán Ibacache-Pulgar & Cristian Villegas & Javier Linkolk López-Gonzales & Magaly Moraga, 2023. "Influence measures in nonparametric regression model with symmetric random errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 1-25, March.
    6. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    7. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.

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