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Original Articles

Empirical likelihood for outlier detection in regression models

, ORCID Icon &
Pages 255-281 | Received 19 Jan 2017, Accepted 18 Jun 2017, Published online: 24 Jul 2017

References

  • Astill, S., D. I. Harvey, and R. Taylor. 2013. A bootstrap test for additive outliers in nonstationary time series. Journal of Time Series Analysis 34:454–65.
  • Atkinson, A. C. 1986. Comments on: Influential observations, high leverage points and outliers in linear regression. Statistical Science 1:397–402.
  • Atkinson, A. C., and M. Riani. 2000. Robust diagnostic regression analysis. New York, NY: Springer.
  • Baragona, R., F. Battaglia, and D. Cucina. 2013. Empirical likelihood for break detection in time series. Electronic Journal of Statistics 7:3089–123.
  • Baragona, R., F. Battaglia, and D. Cucina. 2016 Empirical likelihood for outlier detection and estimation in autoregressive time series. Journal of Time Series Analysis 37:315–36.
  • Barnett, V., and T. Lewis. 1978. Outliers in statistical data. New York, NY: Wiley.
  • Bartlett, M. S. 1951. An inverse matrix adjustment arising in discriminant analysis. Annals of Mathematical Statistics 22:107–11.
  • Belsley, D. A., E. Kuh, and R. E. Welsch. 1980. Regression diagnostics: Identifying influential data and sources of collinearity. New York, NY: Wiley.
  • Billor, N., and G. Kiral. 2008. A comparison of multiple outlier detection methods for regression data. Communications in Statistics—Simulation and Computation 37:521–45.
  • Bondell, H. D., and L. A. Stefanski. 2013. Efficient robust regression via two-stage generalized empirical likelihood. Journal of the American Statistical Association 108:644–55.
  • Chen, S. X., and I. Van Keilegom. 2009. A review on empirical likelihood methods for regression. Test 18:415–47.
  • Chuang, C.-S., and N. H. Chan. 2002. Empirical likelihood for autoregressive models, with applications to unstable time series. Statistica Sinica 12:387–407.
  • Ciuperca, G. 2013. Empirical likelihood for nonlinear models with missing responses. Journal of Statistical Computation and Simulation 83:739–58.
  • Cook, R. D. 1977. Detection of influential observation in linear regression. Technometrics 19:15–18.
  • Cook, R. D. 1986. Assessment of local influence. Journal of the Royal Statistical Society B 48:133–69.
  • Cook, R. D., and S. Weisberg. 1982. Residuals and influence in regression. Boca Raton, FL: Chapman and Hall/CRC.
  • DiCiccio, T. J., and A. C. Monti. 2001. Approximations to the profile empirical likelihood function for a scalar parameter in the context of M-estimation. Biometrika 88:337–51.
  • Hadi, A. S. 1992. A new measure of overall potential influence in linear regression. Computational Statistics and Data Analysis 14:1–27.
  • Hadi, A. S., and J. S. Simonoff. 1993. Procedures for identification of outliers in linear models. Journal of the American Statistical Association 88:1264–72.
  • Hjort, N. L., I. W. McKeague, and I. Van Keilegom. 2009. Extending the scope of empirical likelihood. Annals of Statistics 37:1079–111.
  • Hoaglin, D. C., and R. E. Welsch. 1978. The hat matrix in regression and ANOVA. American Statistician 32:17–22.
  • Hoeting, J., A. E. Raftery, and D. Madigan. 1996. A method for simultaneous variable selection and outlier identification in linear regression. Computational Statistics and Data Analysis 22:251–70.
  • Imon, A. H. M. R., and M.M. Ali. 2005. Bootstrapping regression residuals. Journal of the Korean Data and Information Science Society 16:665–82.
  • Kitamura, Y. 1997. Empirical likelihood methods for weakly dependent processes. Annals of Statistics 25:2084–102.
  • Kolaczyk, E. D. 1994. Empirical likelihood for generalized linear models. Statistica Sinica 4:199–218.
  • Lazar, N. 2005. Assessing the effect of individual data points on inference from empirical likelihood. Journal of Computational and Graphical Statistics 14:626–42.
  • Menjoge, R. S., and R. E. Welsch. 2010. A diagnostic method for simultaneous feature selection and outlier identification in linear regression. Computational Statistics and Data Analysis 54:3181–93.
  • Michaelis, L., and M. L. Menten. 1913. Die kinetik der invertinwirkung. Biochemische Zeitschrift 49:333–69.
  • Monti, A. C. 1997. Empirical likelihood confidence regions in time series models. Biometrika 84:395–405.
  • Mykland, P. A. 1995. Dual likelihood. Annals of Statistics 23:396–421.
  • Niu, C., X. Guo, W. Xu, and L. Zhu. 2014. Empirical likelihood inference in linear regression with nonignorable missing response. Computational Statistics and Data Analysis 79:91–112.
  • Nordman, D. J., and S. N. Lahiri. 2006. A frequency domain empirical likelihood for short- and long-range dependence. Annals of Statistics 34:3019–50.
  • Nordman, D. J., and S. N. Lahiri. 2014. A review of empirical likelihood methods for time series. Journal of Statistical Planning and Inference 155:1–18.
  • Nurunnabi, A. A. M., M. Nasser, and A. H. M. R. Imon. 2016. Identification and classification of multiple outliers, high leverage points and influential observations in linear regression. Journal of Applied Statistics 43:509–25.
  • Owen, A. B. 1988. Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75:237–49.
  • Owen, A. B. 1990. Empirical likelihood ratio confidence regions. Annals of Statistics 18:90–120.
  • Owen, A. B. 1991. Empirical likelihood for linear models. Annals of Statistics 19:1725–47.
  • Owen, A. B. 2001. Empirical likelihood. Boca Raton, FL: Chapman and Hall/CRC.
  • Peña, D., and V. Yohai. 1995. The detection of influential subsets in linear regression by using an influence matrix. Journal of the Royal Statistical Society B 57:145–56.
  • Piyadi Gamage, R. D., W. Ning, and A. K. Gupta. 2017. Adjusted empirical likelihood for long-memory time series models. Journal of Statistical Theory and Practice 11:220–33.
  • Plackett, R. L. 1950. Some theorems in least squares. Biometrika 37:149–57.
  • Qin, J., and J. Lawless. 1994. Empirical likelihood and general estimating equations. Annals of Statistics 22:300–25.
  • Rosner, B. 1975. On the detection of many outliers. Technometrics 17:217–27.
  • Salloum, Z. 2016. Empirical likelihood confidence regions for the parameters of a two phases nonlinear model with and without missing response data. Journal of Statistical Theory and Practice 10:612–38.
  • Swallow, W., and F. Kianifard. 1996. Using robust scale estimates in detecting multiple outliers in linear regression. Biometrics 52:545–56.
  • Tang, N.-S., and P.-Y. Zhao. 2013. Empirical likelihood-based inference in nonlinear regression models with missing responses at random. Statistics 47:1141–59.
  • Tsao, M., and J. Zhou. 2001. On the robustness of empirical likelihood ratio confidence intervals for location. Canadian Journal of Statistics 29:129–40.
  • Van Keilegom, I., C. S. Sellero, and W. G. Manteiga. 2008. Empirical likelihood based testing for regression. Electronic Journal of Statistics 2:581–604.
  • Vexler, A., A. D. Hutson, and X. Chen. 2016. Statistical testing strategies in the health sciences. New York, NY: Chapman and Hall/CRC.
  • Vexler, A., J. Yu, Y. Zhao, and G. Gurevich. 2017. Expected p-values in light of an ROC curve analysis applied to optimal multiple testing procedures. Statistical Methods in Medical Research. In press.
  • Wei, W. H., and W. K. Fung. 1999. The mean-shift outlier model in general weighted regression and its applications. Computational Statistics and Data Analysis 30:429–41.
  • Wells, W. T., R. L. Anderson, and J. W. Cell. 1962. The distribution of the product of two central or non central chi-square variates. Annals of Mathematical Statistics 33:1016–20.
  • Willems, G., and S. V. Aelst. 2005. Fast and robust bootstrap for LTS. Computational Statistics and Data Analysis 48:703–15.
  • Wisnowski, J. W., D. C. Montgomery, and J. R. Simpson. 2001. A comparative analysis of multiple outlier detection procedures in the linear regression model. Computational Statistics and Data Analysis 36:351–82.
  • Wu, C. F. J. 1986. Jackknife, bootstrap and other resampling methods in regression analysis. Annals of Statistics 14:1261–95.
  • Zhu, H., J. G. Ibrahim, N. Tang, and H. Zhang. 2008. Diagnostic measures for empirical likelihood of general estimating equations. Biometrika 95:489–507.

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