Outlier Detection Under Star-Contoured Errors

References

• Aitkin, M., and G. Wilson. 1980. Mixture models, outliers, and the EM algorithm. Technometrics, 22, 325–331.
   Web of Science ®Google Scholar
• Atkinson, A. C. 1985. Plots, transformations, and regression. Oxford, UK: Oxford University Press.
   Google Scholar
• Baksalary, J. K., and S. Puntanen. 1990. A complete solution to the problem of robustness of Grubbs’ test. Can. J. Stat., 18, 285–287.
   Web of Science ®Google Scholar
• Barnett, V., and T. Lewis. 1994. Outliers in statistical data, 3rd ed. New York, NY: Wiley.
   Google Scholar
• Beckman. R. J., and H. J. Trussell. 1974. The distribution of an arbitrary Studentized residual and the effects of updating in multiple regression. J. Am. Stat. Assoc., 69, 199–201.
   Web of Science ®Google Scholar
• Belsley, D. A., E. Kuh, and R. E. Welsch. 1980. Regression diagnostics: Identifying influential data and sources of collinearity. New York, NY: Wiley.
   Google Scholar
• Bendre, S. M., and B. K. Kale. 1987. Masking effect on tests for outliers in normal samples. Biometrika, 74, 891–896.
   Web of Science ®Google Scholar
• Box, G. E. P., and G. C. Tiao. 1968. A Bayesian approach to some outlier problems. Biometrika, 55, 119–129.
   PubMed Web of Science ®Google Scholar
• Chatterjee, S., and A. S. Hadi. 1988. Sensitivity analysis in linear regression. New York, NY: Wiley.
   Google Scholar
• Cook, R. D., and S. Weisberg. 1982. Residuals and influence in regression, London, UK: Chapman and Hall.
   Google Scholar
• DasGupta, A. 2013. Anirban’s angle: 215 Influential developments in statistics. IMS Bull., 42(8), 10–11.
   Google Scholar
• Dharmadhikari, S., and K. Joag-Dev. 1988. Unimodality, convexity, and applications. New York, NY: Academic Press.
   Google Scholar
• Dixon, W. J. 1950. Analysis of extreme values. Ann. Math. Stat., 21, 488–506.
   Google Scholar
• Dixon, W. J. 1951. Ratios involving extreme values. Ann. Math. Stat., 22, 68–78.
   Google Scholar
• Ennis, D., and N. Johnson. 1993. Noncentral and central chi-square, F, and beta distribution functions as special cases of the distribution function of an indefinite quadratic form. Commun. Stat. Theory Methods, 22, 897–905.
   Web of Science ®Google Scholar
• Fang, K. T., S. Kotz, and K. W. Ng. 1990. Symmetric multivariate and related distributions. London, UK: Chapman and Hall.
   Google Scholar
• Fang, K. T., and Y. T. Zhang. 1990. Generalized multivariate analysis. New York, NY: Springer-Verlag.
   Google Scholar
• Ferguson, T. S. 1961. On the rejection of outliers. Proc. 4th Berkeley Symp., 1, 253–287.
   Google Scholar
• Fisher, R. A. 1960. The design of experiments, 8th ed. Edinburgh, UK: Oliver and Boyd.
   Google Scholar
• Fox, J. 1991. Regression diagnostics. Newbury Park, CA: Sage.
   Google Scholar
• Grubbs, F. E. 1950. Criteria for testing outlying observations. Ann. Math. Stat., 21, 27–58.
   Google Scholar
• Grubbs, F. E. 1969. Procedures for detecting outlying observations in samples. Technometrics, 11, 1–21.
   Web of Science ®Google Scholar
• Grubbs, F. E., and G. Beck. 1972. Extension of sample sizes and percentage points for significance tests of outlying observations. Technometrics, 14, 847–854.
   Web of Science ®Google Scholar
• Hoaglin, D. C., and P. J. Kempthorne. 1986. Influential observations, high leverage points, and outliers in linear regression: Comment. Stat. Sci., 1, 408–412.
   Google Scholar
• Imhof, J. 1961. Computing the distribution of quadratic forms in normal variables. Biometrika, 48, 419–426.
   Web of Science ®Google Scholar
• Jensen, D. R. 1981. Power of invariant tests for linear hypotheses under spherical symmetry. Scand. J. Stat., 8, 169–174.
   Web of Science ®Google Scholar
• Jensen, D. R. 1985. Multivariate distributions. In Encyclopedia of statistical sciences, vol. 6, ed. N. L. Johnson, S. Kotz, and C. B. Read, 43–55. New York, NY: Wiley.
   Google Scholar
• Jensen, D. R., 1996. Structured dispersion and validity in linear inference. Linear Algebra Appl., 249, 189–196.
   Web of Science ®Google Scholar
• Jensen, D. R. 2000. The use of studentized diagnostics in regression, Metrika, 52, 213–223.
   Web of Science ®Google Scholar
• Jensen, D. R. 2001. Properties of selected subset diagnostics in regression. Stat. Prob. Lett., 51, 377–388.
   Web of Science ®Google Scholar
• Jensen, D. R., and I. J. Good. 1981. Invariant distributions associated with matrix laws under structural symmetry. J. R. Statist. Soc. B, 43, 327–332.
   Google Scholar
• Jensen, D. R., and D. E. Ramirez. 2009. Anomalies in the analysis of calibrated data. J. Stat. Comput. Sim., 79, 299–314.
   Web of Science ®Google Scholar
• Jensen, D. R., and D. E. Ramirez. 2012. Irregularities in X(Y) from Y(X) in linear regression. J. Stat. Comput. Sim., 83, 1807–1828.
   Web of Science ®Google Scholar
• Jensen, D. R., and D. E. Ramirez. 2014. Noncentralities induced in regression diagnostics. J. Statist. Theory & Pract., 8, 1–25.
   Google Scholar
• Kanter, M. 1977. Unimodality and dominance for symmetric random vectors. Trans. Am. Math. Soc., 229, 65–85.
   Web of Science ®Google Scholar
• Kariya, T., and B. K. Sinha. 1989. Robustness of statistical tests. New York, NY: Academic Press.
   Google Scholar
• Martin, M. A., S. Roberts, and L. Zheng. 2010. Delete-2 and delete-3 jackknife procedures for unmasking in regression. Aust. NZ J. Stat., 52, 45–60.
   Web of Science ®Google Scholar
• Mathai, A. M., and S. B. Provost. 1992. Quadratic forms in random variables: Theory and applications. New York, NY: Marcel Dekker.
   Google Scholar
• Myers, R. H. 1990. Classical and modern regression with applications, 2nd ed. Boston, MA: PWS-Kent.
   Google Scholar
• Nair, K. R., 1948. The distribution of the extreme deviate from the sample mean and its Studentized form. Biometrika, 35, 118–144.
   PubMed Web of Science ®Google Scholar
• Nandi, S. B., and S. Choudhury. 2002. Series representation of doubly noncentral t distribution by use of the Mellin integral transform. Commun. Stat. Theory Methods, 31, 2139–2149.
   Web of Science ®Google Scholar
• Rorabacher, D. 1991. Statistical treatment for rejection of deviant values: Critical values of Dixon’s “Q” parameter and related subrange ratios at the 95% confidence level. Anal. Chem., 63, 139–146.
   Web of Science ®Google Scholar
• Rousseeuw, P. J., and A. M. Leroy. 1987. Robust regression and outlier detection. New York, NY: Wiley.
   Google Scholar
• Sherman, S. 1955. A theorem on convex sets with applications. Ann. Math. Stat., 26, 763–766.
   Google Scholar
• Shiffler, R. 1988. Maximum Z scores and outliers. Am. Stat., 42, 79–80.
   Web of Science ®Google Scholar
• Snedecor, G. W., and W. G. Cochran. 1968. Statistical methods, 6th ed. Ames, IA: Iowa State University Press.
   Google Scholar
• Srivastava, M. S. 1980. Effect of equicorrelation in detecting a spurious observation. Can. J. Stat.., 8, 249–251.
   Google Scholar
• Thompson, W. R. 1935. On a criterion for the rejection of observations and the distribution of the ratio of deviation to sample standard deviation. Ann. Math. Stat., 6, 214–219.
   Google Scholar
• Ullah, M. A., and G. R. Pasha. 2009. The origin and developments of influence measures in regression. Pak. J. Stat., 25, 295–307.
   Web of Science ®Google Scholar
• Verhoeven, P., and M. McAleer. 2004. Fat tails and asymmetry in financial volatility models. Math. Comput. Simulat., 64, 351–361.
   Web of Science ®Google Scholar
• Verma, S. P., and A. Quiroz-Ruiz. 2006. Critical values for six Dixon tests for outliers in normal samples up to sizes 100, and applications in science and engineering. Rev. Mex. Cienc. Geol., 23, 133–161.
   Web of Science ®Google Scholar
• Woodward, W., and S. R. Sain. 2003. Testing for outliers from a mixture distribution when some data is missing. Comput. Stat. Data Anal., 44, 193–210.
   Web of Science ®Google Scholar
• Young, D. M., R. Pavur, and V. R. Marco. 1989. On the effect of correlation and unequal variances in detecting a spurious observation. Can. J. Stat., 17, 103–105.
   Web of Science ®Google Scholar