Skip to main content
Log in

Nonparametric inference on the difference of location parameters of correlated variables from fragmentary samples

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

In this paper, two types of robust estimators and approximate confidence intervals for the difference of location parameters of correlated random variables are proposed and investigated when some observations are missing. It is shown that the suggested estimators are consistent and asymptotically normally distributed. In addition, the proposed approximate confidence intervals are also shown to enjoy some nice asymptotic properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson, T. W. (1957). Maximum likelihood estimates for multivariate normal distribution when some observations are missing,J. Amer. Statist. Ass.,52, 200–214.

    Article  MathSciNet  Google Scholar 

  2. Boos, D. (1980). A new method for constructing approximate confidence intervals,J. Amer. Statist. Ass.,75, 142–145.

    MathSciNet  MATH  Google Scholar 

  3. Boos, D. and Serfling, R. J. (1980). A note on differentials and CLT and LIL for statistical functions with application toM-estimates,Ann. Statis.,8, 618–624.

    Article  Google Scholar 

  4. Geertsema, J. C. (1970). Sequential confidence intervals based on rank tests,Ann. Math. Statist.,41, 1016–1026.

    Article  MathSciNet  Google Scholar 

  5. Gupta, A. K. and Rohatgi, V. K. (1978). Inference on the difference of means of correlated variables from fragmentary samples,Sankhyã, B40, 49–64.

    MathSciNet  MATH  Google Scholar 

  6. Hampel, F. R. (1968).Contributions to the Theory of Robust Estimation, Ph.D. dissertation University of California, Berkeley.

    Google Scholar 

  7. Hampel, F. R. (1974). The influence curve and its roles in robust estimation,J. Amer. Statist. Ass.,69, 383–397.

    Article  MathSciNet  Google Scholar 

  8. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables,J. Amer. Statist. Ass.,58, 13–30.

    Article  MathSciNet  Google Scholar 

  9. Huber, P. J. (1964). Robust estimation of a location parameter,Ann. Math. Statist.,35, 73–101.

    Article  MathSciNet  Google Scholar 

  10. Lin, P. E. (1971). Estimation procedures for difference of means with missing data,J. Amer. Statist. Ass.,66, 634–636.

    Article  Google Scholar 

  11. Lin, P. E. (1973). Procedures for testing the difference of means with incomplete data,J. Amer. Statist. Ass.,68, 699–703.

    Article  Google Scholar 

  12. Lin, P. E. and Stivers, L. E. (1974). On difference of means with incomplete data,Biometrika,61, 325–334.

    Article  MathSciNet  Google Scholar 

  13. Mehta, J. S. and Gurland, J. (1969). Some properties and an application of a statistic arising in testing correlation,Ann. Math. Statist.,40, 1736–1745.

    Article  MathSciNet  Google Scholar 

  14. Serfling, R. J. (1980).Approximation Theorems of Mathematical Statistics, Wiley, New York.

    Book  Google Scholar 

  15. Wei, L. J. (1981). Estimation of location difference for fragmentary samples,Biometrika,68, 471–476.

    Article  MathSciNet  Google Scholar 

  16. Wilks, S. S. (1932). Moments and distributions of estimates of population parameters from fragmentary samples,Ann. Math. Statist.,3, 163–203.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Cheng, K.F. Nonparametric inference on the difference of location parameters of correlated variables from fragmentary samples. Ann Inst Stat Math 39, 331–347 (1987). https://doi.org/10.1007/BF02491472

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02491472

Key words and phrases

Navigation