A multiple-case deletion approach for detecting influential points in high-dimensional regression

References

• Alfons, A., and S. Gelper. 2013. Sparse least trimmed squares regression for analyzing high-dimensional large data sets. Annals of Applied Statistics 7 (1):226–48.
   Google Scholar
• Barnett, V., and T. Lewis. 1994. Outliers in statistical data. 3rd ed. New York: Wiley.
   Google Scholar
• Becker, C., and U. Gather. 2001. The largest nonidentifiable outlier: A comparison of multivariate simultaneous outlier identification rules. Computational Statistics and Data Analysis 36 (1):119–27.
   Google Scholar
• Belsley, D. A., E. Kuh, and R. Welsch. 1980. Regression diagnostics: Identifying influential data and sources of collinearity. New York: Wiley.
   Google Scholar
• Chatterjee, S., and A. S. Hadi. 1988. Sensitivity analysis in linear regression. New York: Wiley.
   Google Scholar
• Cook, R. D. 1977. Detection of influential observation in linear regression. Technometrics 19 (1):15–18.
   Google Scholar
• Cook, R. D. 1979. Influential observations in linear regression. Journal of the American Statistical Association 74 (365):169–74.
   Google Scholar
• Cook, R. D., and S. Weisberg. 1982. Residuals and influence in regression. New York-London: Chapman and Hall.
   Google Scholar
• Davies, L., and U. Gather. 1993. The identification of multiple outliers. Journal of the American Statistical Association 88 (423):782–92.
   Google Scholar
• Fan, J., and J. Lv. 2008. Sure independence screening for ultrahigh dimensional feature space (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70 (5):849–911.
   Google Scholar
• Hadi, A. S., and J. S. Simonoff. 1993. Procedures for the identification of multiple outliers in linear models. Journal of the American Statistical Association 88 (424):1264–72.
   Google Scholar
• Hawkins, D. 1980. Identification of outliers. New York: Chapman and Hall.
   Google Scholar
• Imon, A. H. M. R. 2005. Identifying multiple influential observations in linear regression. Journal of Applied Statistics 32 (9):929–46.
   Google Scholar
• Li, R., W. Zhong, and L. Zhu. 2012. Feature screening via distance correlation learning. Journal of the American Statistical Association 107 (499):1129–39.
   Google Scholar
• Nurunnabi, A. A. M., A. S. Hadi, and A. H. M. R. Imon. 2014. Procedures for the identification of multiple influential observations in linear regression. Journal of Applied Statistics 41 (6):1315–31.
   Google Scholar
• Oshima, R. G., H. Baribault, and C. Cauln. 1996. Oncogenic regulation and function of keratins 8 and 18. Cancer and Metastasis Reviews 15 (4):445–71.
   Google Scholar
• Pena, D. 2005. A new statistic for influence in linear regression. Technometrics 47 (1):1–12.
   Google Scholar
• Pena, D., and V. Yohai. 1999. A fast procedure for outlier diagnostics in large regression problems. Journal of the American Statistical Association 94 (446):434–45.
   Google Scholar
• Roberts, S., M. A. Martin, and L. Zheng. 2015. An adaptive, automatic multiple-case deletion technique for detecting influence in regression. Technometrics 57 (3):408–17.
   Google Scholar
• Rousseeuw, P. J., and A. M. Leroy. 1987. Robust regression and outlier detection. New York: Wiley.
   Google Scholar
• Shankavaram, U. T., W. C. Reinhold, S. Nishizuka, S. Major, D. Morita, K. K. Chary, M. A. Reimers, U. Scherf, A. Kahn, D. Dolginow, J. Cossman, E. P. Kaldjian, D. A. Scudiero, E. Petricoin, L. Liotta, J. K. Lee, and J. N. Weinstein. 2007. Transcript and protein expression profiles of the NCI-60 cancer cell panel: An integromic microarray study. Molecular Cancer Therapeutics 6 (3):820–32.
   Google Scholar
• Székely, G. J., M. L. Rizzo, and N. K. Bakirov. 2007. Measuring and testing dependence by correlation of distances. The Annals of Statistics. 35 (6):2769–94.
   Google Scholar
• Zhao, J., C. Leng, L. Li, and H. Wang. 2013. High-dimensional influence measure. Annals of Statistics 41 (5):2639–67.
   Google Scholar
• Zhao, J., C. Liu, L. Niu, and C. Leng. 2016. Multiple Influential Point Detection in High-dimensional Spaces. https://arxiv.org/abs/1609.03320.
   Google Scholar
• Zou, C., S. Tseng, and Z. Wang. 2014. Outlier detection in general profiles using penalized regression method. IIE Transactions 46:106–17.
   Google Scholar