Robust Inference for Testing Order-Restricted Inference

Kang, Moon-Su

  • Published : 2009.10.31


Classification of subjects with unknown distribution in small sample size setup may involve order-restricted constraints in multivariate parameter setups. Those problems makes optimality of conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Redescending M-estimator along with that principle yields a considerably appropriate robust testing procedure. Furthermore, conditionally distribution-free test based upon exact permutation theory is used to generate p-values, even in small sample. Applications of this method are illustrated in simulated data and read data example (Lobenhofer et al., 2002)


Redescending M-estimator;union-intersection principle;distribution-free


  1. Andrews, D. F. (1974). A Robust method for multiple linear regression, Technometrics, 16, 523-531
  2. Huber, P. J. (1973). Robust regression: Asymptotics, conjectures and Monte Carlo, The Annals of Statistics. 1, 799-821
  3. Huber, P. J. (1977). Robust methods of estimation of regression coefficients, Statistics, 8, 41-53
  4. Huber, P. J. (1981). Robust Statistics, Wiley, New York
  5. Huber, P. J. and Dutter, R. (1974). Numerical solution of robust regression problem, In Proceedings of the Symposium on Computational Statistics, Physika Verlag, Vienna, 165-172
  6. Lobenhofer, E. K., Bennett, L., Cable, P. L., Li, L., Bushel, P. R. and Afshari, C. A. (2002). Regulation of DNA replication fork genes by 17Beta-estradiol, Molecular Endocrinology, 16, 1215-1229
  7. Maronna, R. A., Martin, D. R. and Yohai, J. V. (2006). Robust Statistics: Theory and Methods, Wiley Series in Probability and Statistics, New York
  8. Rousseeuw, P. J. and Yohai, V. J. (1984). Robust regression by means of S-estimators, In Robust and Nonlinear Time Series Analysis, Lecture Notes in Statistics, 26, Springer-Verlag, (Berlin/New York) 256-272
  9. Roy, S. N. (1953). On a heuristic method of test construction and its use in multivariate analysis, The Annals of Mathematical Statistics, 24, 220-238
  10. Silvapulle, M. J. (1985). Asymptotic behavior of robust estimators of regression and scale parameters with fixed carriers, The Annals of Statistics, 13, 1490-1497
  11. Siegel, A F. (1982). Robust regression using repeated' medians, Biometrika, 69, 242-244