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Some Comments on Quantiles and Order Statistics

Published online by Cambridge University Press:  20 November 2018

P. V. Ramachandramurty  and
M. Sudhakara Rao
P. V. Ramachandramurty
Affiliation:
University of Alberta, Edmonton, Alberta
M. Sudhakara Rao
Affiliation:
University of Alberta, Edmonton, Alberta
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A new concept—that of pseudoconsistency—which seems to be particularly appropriate for the estimation of a quantile is introduced. It is shown without any conditions whatsoever on the underlying distributionthat the sample quantile is strongly pseudoconsistent for the corresponding population quantile. The asymptotic distribution of the sample quantiles and order statistics is derived when the underlying distribution is discrete.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 289 - 293
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Cramer, H., Mathematical methods of statistics, Princeton Univ. Press, Princeton, N.J., 1951.Google Scholar
2. David, H. A., Order statistics, Wiley, New York, 1970.Google Scholar
3. Feldman, D. and Tucker, H. G., Estimation of non-unique quantités, Ann. Math. Stat. 37 (1966), 451–457.Google Scholar
4. Kabe, D. G., Some distribution problems of order statistics from discrete populations, Ann. Inst. Math. Statist. (1970), 551–556.Google Scholar
5. Loève, M., Probability theory, Van Nostrand, Princeton, N.J., 1960.Google Scholar
6. Mosteller, F., On some useful inefficient statistics, Ann. Math. Stat., 17 (1946), 377–408.Google Scholar
7. Rao, C. R., Linear statistical inference and its applications, Wiley, New York, 1965.Google Scholar