Use of likelihood ratio tests to detect outliers under the variance shift outlier model

References

• A.C. Atkinson, Plots, Transformations and Regression, Clarendon Press, Oxford, 1985.
   Google Scholar
• V. Barnett and T. Lewis, Outliers in Statistical Data, 3rd ed., John Wiley & Sons, New York, 1994.
   Google Scholar
• D.A. Belsley, E. Kuh, and R.E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Wiley, New York, 1980.
   Google Scholar
• G.E.P Box and G.C. Tiao, A Bayesian approach to some outlier problems, Biometrika 55 (1968), pp. 119–129. doi: 10.1093/biomet/55.1.119
   PubMed Web of Science ®Google Scholar
• R. Christensen, L.M. Pearson, and W. Johnson, Case-deletion diagnostics for mixed models, Technometrics 34 (1992), pp. 38–45. doi: 10.2307/1269550
   Web of Science ®Google Scholar
• R.D. Cook, Detection of influential variables in linear regression, Technometrics 19 (1977), pp. 15–18.
   Web of Science ®Google Scholar
• R.D. Cook, Assessment of local influence (with discussion), J. Roy. Stat. Soc. Ser. B 48 (1986), pp. 133–169.
   Google Scholar
• R.D. Cook, N. Holschuh, and S. Weisberg, A note on an alternative outlier model, J. Roy. Stat. Soc. Ser. B 44 (1982), pp. 370–376.
   Google Scholar
• R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman and Hall, New York, 1982.
   Google Scholar
• C.M. Crainiceanu and D. Ruppert, Likelihood ratio tests in linear mixed models with one variance component, J. Roy. Stat. Soc. Ser. B 66 (2004), pp. 165–185. doi: 10.1111/j.1467-9868.2004.00438.x
   Google Scholar
• A.R. Gilmour, R. Thompson, and B.R. Cullis, Average information REML: An efficient algorithm for variance parameter estimation in linear mixed models, Biometrics 51 (1995), pp. 1440–1450. doi: 10.2307/2533274
   Web of Science ®Google Scholar
• F.N Gumedze, A variance shift model for outlier detection and estimation in linear and linear mixed models, Ph.D. thesis, Department of Statistical Sciences, University of Cape Town, 2009.
   Google Scholar
• F.N. Gumedze, S.J. Welham, B.J. Gogel, and R. Thompson, A variance shift model for detection of outliers in the linear mixed model, Comput. Statist. Data Anal. 54 (2010), pp. 2128–2144. doi: 10.1016/j.csda.2010.03.019
   Web of Science ®Google Scholar
• G. Hall, W.H. Rogers, and D Pregibon, Outliers matter in survival analysis, Tech. Rep. P-6761, Rand, Santa Monica, CA, 1982.
   Google Scholar
• F.R. Hampel, E.M. Ronchetti, P.J. Rouseeuw, and W.A. Stahel, Robust Statistics: The Approach Based on Influence Functions, Wiley, New York, 1986.
   Google Scholar
• J. Hoeting, A.E. Raftery, and D. Madigan, A method for simultaneous variable selection and outlier identification in linear regression, Comput. Stat. Data Anal. 22 (1996), pp. 251–270. doi: 10.1016/0167-9473(95)00053-4
   Web of Science ®Google Scholar
• D.W. Hosmer and S. Lemeshow, Applied Logistic Regression, John Wiley, New York, 1989.
   Google Scholar
• P.J. Huber, Robust Statistics, Wiley, New York, 1981.
   Google Scholar
• P.J. Huber and E.M. Ronchetti, Robust Statistics, 2nd ed. John Wiley & Sons, Hoboken, NJ, 2009.
   Google Scholar
• H.C. Jing, D. Kornyukhin, K. Kanyuka, S. Orford, A. Zlatska, O.P. Mitrofanova, R. Koebner, and K. Hammond-Kosack, Identification of variation in adaptively important traits and genome-wide analysis of trait–marker associations in Triticum monococcum, J. Exper. Bot. 58 (2007), pp. 3749–3764. doi: 10.1093/jxb/erm225
   PubMed Web of Science ®Google Scholar
• A. Justel and D. Pena, Bayesian unmasking in linear models, Comput. Stat. Data Anal. 36 (2001), pp. 69–84. doi: 10.1016/S0167-9473(00)00033-5
   Web of Science ®Google Scholar
• D.L. Mohr, Bayesian identification of clustered outliers in multiple regression, Comput. Stat. Data Anal. 51 (2007), pp. 3955–3967. doi: 10.1016/j.csda.2006.04.008
   Web of Science ®Google Scholar
• D. Pregibon, Logistic regression diagnostics, Ann. Statist. 9 (1981), pp. 705–724. doi: 10.1214/aos/1176345513
   Web of Science ®Google Scholar
• P.J. Rousseeuw, Least median squares regression, J. Amer. Stat. Assoc. 79 (1984), pp. 871–880. doi: 10.1080/01621459.1984.10477105
   Web of Science ®Google Scholar
• P.J. Rousseeuw and A.M. Leroy, Robust Regression and Outlier Detection, John Wiley, New York, 1987.
   Google Scholar
• S.G. Self and K.Y. Liang, Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions, J. Amer. Stat. Assoc. 82 (1987), pp. 605–610. doi: 10.1080/01621459.1987.10478472
   Web of Science ®Google Scholar
• B. Storer and J. Crowley, A diagnostic for Cox regression and general conditional likelihoods, J. Amer. Stat. Assoc. 80 (1985), pp. 139–147. doi: 10.1080/01621459.1985.10477153
   Web of Science ®Google Scholar
• D. Stram and J.W. Lee, Variance components testing in longitudinal mixed effects model, Biometrics 50 (1994), pp. 1171–1177. doi: 10.2307/2533455
   PubMed Web of Science ®Google Scholar
• D. Stram and J.W. Lee, Correction to ‘Variance components testing in longitudinal mixed effects model’, Biometrics 51 (1995), pp. 1196.
   Web of Science ®Google Scholar
• R. Thompson, A note on restricted maximum likelihood estimation with an alternative outlier model, J. Roy. Stat. Soc. Ser. B 47 (1985), pp. 53–55.
   Google Scholar
• S.J. Welham, S.A. Gezan, S.J. Clark, and A. Mead, Statistical Methods in Biology: Design and Analysis of Experiments and Regression, Chapman and Hall, Oxford, 2014.
   Google Scholar