The Annals of Statistics

Regression rank scores estimation in ANOCOVA

Pranab Kumar Sen

Full-text: Open access

Abstract

In semiparametric ANOCOVA (mixed-effects) models, the role of regression rank scores in robust estimation of fixed-effects parameters as well as covariate regression functionals is critically appraised, and the relevant asymptotic theory is presented.

Article information

Source
Ann. Statist., Volume 24, Number 4 (1996), 1586-1601.

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032298286

Digital Object Identifier
doi:10.1214/aos/1032298286

Mathematical Reviews number (MathSciNet)
MR1416651

Zentralblatt MATH identifier
0898.62087

Subjects
Primary: 62G05: Estimation 62J05: Linear regression

Keywords
Asymptotic efficiency and representation covariate regression functional heteroscedasticity regression quantiles $R$-estimators semiparametric models stochastic predictors weak invariance principles

Citation

Sen, Pranab Kumar. Regression rank scores estimation in ANOCOVA. Ann. Statist. 24 (1996), no. 4, 1586--1601. doi:10.1214/aos/1032298286. https://projecteuclid.org/euclid.aos/1032298286


Export citation

References

  • ANSCOME, F. J. 1952. Large sample theory of sequential estimation. Proc. Cambridge Philos. Soc. 48 600 607. Z.
  • BHATTACHARy A, P. K. and GANGOPADHy AY, A. K. 1990. Kernel and nearest neighbor estimation of a conditional quantile. Ann. Statist. 18 1400 1415. Z.
  • BICKEL, P. J. and WICHURA, M. J. 1971. Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42 1656 1670. Z.
  • DOKSUM, K. 1969. Starshaped transformations and power of rank tests. Ann. Math. Statist. 40 1167 1176. Z.
  • GANGOPADHy AY, A. K. and SEN, P. K. 1992. Contiguity in nonparametric estimation of a Z conditional functional. In Nonparametric Statistics and Related Topics A. K. M. E.. Saleh, ed. 141 162. North-Holland, Amsterdam. Z.
  • GANGOPADHy AY, A. K. and SEN, P. K. 1993. Contiguity in Bahadur-ty pe representations of a conditional quantile and application in conditional quantile processes. In Statistics Z and Probability, a Raghu Raj Bahadur Festschrift J. K. Ghosh, S. K. Mitra, K. R.. Parthasarathy and B. L. S. Prakasa Rao, eds. 219 231. Wiley Eastern, New Delhi. Z.
  • GHOSH, M. and SEN, P. K. 1971. On a class of rank order tests for regression with partially informed stochastic predictors. Ann. Math. Statist. 42 650 661. Z.
  • GUTENBRUNNER, C. and JURECKOVA, J. 1992. Regression rank scores and regression quantiles. ´ Ann. Statist. 20 305 330.
  • HAJEK, J. and SIDAK, Z. 1967. Theory of Rank Tests. Academia, Prague. ´ ´ Z.
  • JURECKOVA, J. 1992. Estimation in a linear model based on regression rank scores. J. Non ´paramet. Statist. 1 197 203. Z.
  • JURECKOVA, J. and SEN, P. K. 1993. Asy mptotic equivalence of regression rank scores estima ´tors and R-estimators in linear models. In Statistics and Probability, a Raghu Raj Z Bahadur Festschrift J. K. Ghosh, S. K. Mitra, K. R. Parthasarathy and B. L. S.. Prakasa Rao, eds. 279 291. Wiley Eastern, New Delhi.
  • JURECKOVA, J. and SEN, P. K. 1996. Robust Statistical Procedures: Asy mptotics and Interrela ´tions. Wiley, New York. Z.
  • KOENKER, R. and BASSETT, G. 1978. Regression quantiles. Econometrica 46 33 50. Z.
  • PURI, M. L. and SEN, P. K. 1985. Nonparametric Methods in General Linear Models. Wiley, New York. Z.
  • SEN, P. K. 1981. Sequential Nonparametrics: Invariance Principles and Statistical Inference. Wiley, New York. Z.
  • SEN, P. K. 1993a. Regression rank scores estimation in ANOCOVA. Technical Report 2117, Institute of Statistics, Univ. North Carolina. Z.
  • SEN, P. K. 1993b. Perspectives in multivariate nonparametrics: conditional functionals and ANOCOVA models. Sankhy a Ser. A 55 516 532. Z.
  • SEN, P. K. 1994. Regression quantiles in nonparametric regression. J. Nonparamet. Statist. 3 237 253. Z.
  • SEN, P. K. and GHOSH, M. 1972. On strong convergence of regression rank statistics. Sankhy a Ser. A. 34 335 348.
  • CHAPEL HILL, NORTH CAROLINA 27599-7400 E-MAIL: pksen@sphrax.sph.unc.edu