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Statistics
A Journal of Theoretical and Applied Statistics
Volume 44, 2010 - Issue 3
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Original Articles

Mahalanobis distance under non-normality

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Pages 275-290 | Received 22 Feb 2008, Published online: 17 Jun 2009

References

  • Bradley , E. L. 1985 . “ Overlapping coefficient ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. and Johnson , N. L. New York : John Wiley .
  • Reiser , B. and Faraggi , D. 1999 . Confidence intervals for the overlapping coefficient: the normal equal variance case . Statistician , 48 : 413 – 418 .
  • Rao , P. S.R.S. and Dorvlo , A. S.S. 1985 . The Jackknife procedure for the probabilities of misclassification . Commun. Stat.-Simul. Comput. , 14 : 774 – 790 .
  • Reiser , B. and Faraggi , D. 1997 . Confidence intervals for the generalized ROC criterion . Biometrics , 53 : 644 – 652 .
  • Hutchinson , T. P. and Lai , C. D. 1990 . Continuous Bivariate Distributions Emphasising Applications , Adelaide : Rumsby Scientific .
  • Islam , M. Q. and Tiku , M. L. 2009 . Multiple linear regression model with stochastic design variables . J. Appl. Stat. , 36
  • Vaughan , D. C. and Tiku , M. L. 2000 . Estimation and hypothesis testing for a non-normal bivariate distribution with applications . J. Math. Comput. Model. , 32 : 53 – 67 .
  • Sazak , H. S. , Tiku , M. L. and Islam , M. Q. 2006 . Regression analysis with a stochastic design variable . Int. Stat. Rev. , 74 : 77 – 88 .
  • Tiku , M. L. , Islam , M. Q. and Sazak , H. S. 2008 . Estimation in bivariate nonnormal distributions with stochastic variance functions . Comput. Stat. Data Anal. , 52 : 1728 – 1754 .
  • Tiku , M. L. 1967 . Estimating the mean and standard deviation from censored normal samples . Biometrika , 54 : 155 – 165 .
  • Tiku , M. L. 1968 . Estimating the parameters of log-normal distribution from censored samples . J. Am. Stat. Assoc. , 63 : 134 – 140 .
  • Tiku , M. L. 1989 . “ Modified likelihood estimation ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. and Johnson , N. L. Supplement Volume , New York : Wiley .
  • Tiku , M. L. and Suresh , R. P. 1992 . A new method of estimation for location and scale parameters . J. Stat. Plan. Inference , 30 : 281 – 292 .
  • Bhattacharyya , G. K. 1985 . The asymptotics of maximum likelihood and related estimators based on type II censored data . J. Am. Stat. Assoc. , 80 : 398 – 404 .
  • Surucu , B. 2006 . Goodness-of-fit tests for multivariate distributions . Commun. Stat.-Theory Methods , 35 : 1319 – 1331 .
  • Tiku , M. L. and Singh , M. 1982 . Robust statistics for testing mean vectors of multivariate distributions . Commun. Stat.-Theory Methods , 11 : 985 – 1001 .
  • Lehmann , E. L. 1986 . Testing Statistical Hypotheses , New York : John Wiley .
  • Tiku , M. L. 1980 . Robustness of MML estimators based on censored samples and robust test statistics . J. Stat. Plan. Inference , 4 : 123 – 143 .
  • Kendall , M. G. and Stuart , A. 1967 . The Advanced Theory of Statistics , Vol. 2 , New York : Hafner Publishing Company .
  • Qumsiyeh , S. B. 2007 . Non-normal bivariate distributions: estimation and hypothesis testing , Ankara : Middle East Technical University . Ph.D. thesis
  • Islam , M. Q. and Tiku , M. L. 2004 . Multiple linear regression model under non-normality . Commun. Stat.-Theory Methods , 33 : 2443 – 2467 .
  • Reiser , B. 2001 . Confidence intervals for the Mahalanobis distance . Commun. Stat.-Simul. Comput. , 30 : 37 – 45 .
  • Pearson , E. S. and Tiku , M. L. 1970 . Some notes on the relationship between the distributions of central and non-central F . Biometrika , 57 : 175 – 179 .
  • Tiku , M. L. , Tan , W. Y. and Balakrishnan , N. 1986 . Robust Inference , New York : Marcel Dekker .
  • Tiku , M. L. and Akkaya , A. D. 2004 . Robust Estimation and Hypothesis Testing , New Delhi : New Age International Publishers (formerly, Wiley Eastern) . Also, Oscar publications. Available at www.alltimebooks.com
  • Oral , E. 2006 . Binary regression with stochastic covariates . Commun. Stat.-Theory Methods , 35 : 1429 – 1447 .
  • Akkaya , A. D. and Tiku , M. L. 2008 . Robust estimation in multiple regression model with non-Gaussian noise . Automatica , 44 : 407 – 417 .
  • Wilks , S. S. 1963 . Multivariate statistical outliers . Sankhya A , 25 : 407 – 426 .
  • Tiku , M. L. and Singh , M. 1981 . “ Testing outliers in multivariate data ” . In Statistical Distributions in Scientific Work , Edited by: Taille , C. Vol. 5, D. , 203 – 218 . New York : Reidel Publishing Company .
  • Vaughan , D. C. 1992 . On the Tiku–Suresh method of estimation . Commun. Stat.-Theory Methods , 21 : 451 – 469 .
  • Vaughan , D. C. 2002 . The generalized secant hyperbolic distribution and its properties . Commun. Stat.-Theory Methods , 31 : 219 – 238 .
  • Dunnett , C. W. 1982 . Robust multiple comparisons . Commun. Stat.-Theory Methods , 11 : 2611 – 2629 .
  • Akkaya , A. D. and Tiku , M. L. 2005 . Time series AR(1) model for short-tailed distributions . Statistics , 39 : 117 – 132 .
  • Senoglu , B. 2005 . Robust 2k factorial design with Weibull error distributions . J. Appl. Stat. , 32 : 1051 – 1066 .
  • Hamilton , L. C. 1992 . Regression with Graphics , California : Brooks/Cole Publishing Company .
  • Abramowitz , M. and Stegun , I. A. 1985 . Handbook of Mathematical Functions , New York : Dover .
  • Puthenpura , S. and Sinha , N. K. 1986 . Modified maximum likelihood method for the robust estimation of system parameters from noisy data . Automatica , 22 : 231 – 235 .
  • Senoglu , B. and Tiku , M. L. 2001 . Analysis of variance in experimental design with nonnormal error distributions . Commun. Stat.-Theory Methods , 30 : 1335 – 1352 .

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