The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Robust Inference for Testing Order-Restricted Inference

  • Published : 2009.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

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)

Keywords

References

  1. Andrews, D. F. (1974). A Robust method for multiple linear regression, Technometrics, 16, 523-531 https://doi.org/10.2307/1267603
  2. Huber, P. J. (1973). Robust regression: Asymptotics, conjectures and Monte Carlo, The Annals of Statistics. 1, 799-821 https://doi.org/10.1214/aos/1176342503
  3. Huber, P. J. (1977). Robust methods of estimation of regression coefficients, Statistics, 8, 41-53 https://doi.org/10.1080/02331887708801356
  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 https://doi.org/10.1210/me.16.6.1215
  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 https://doi.org/10.1214/aoms/1177729029
  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 https://doi.org/10.1214/aos/1176349750
  11. Siegel, A F. (1982). Robust regression using repeated' medians, Biometrika, 69, 242-244 https://doi.org/10.1093/biomet/69.1.242