Joanna Kisielińska
ARTICLE

(Polish) PDF

ABSTRACT

The article presents the results of the use of exact percentiles methods for estimating median. For a sample with an odd number of observations used estimator in the form of the sample median (standard estimator), and for a sample with an even number of observations, used estimator in the form of the sample median and standard estimator. It presents a formula defining the distribution of standard estimator and describes how you can determine the distribution of the estimator in the form of the sample median for sample with an even number of observations. The study was conducted for the selected distributions and selected sample size. It was estimated standard deviation and confidence intervals for selected estimators. The study shows, that the use of exact percentiles method for standard estimators is much simpler than using the classical method with the resampling.

KEYWORDS

exact percentiles method, median estimating

REFERENCES

Baszczyńska A., Pekasiewicz D., (2010), Selected MethodS of Interval Estimation of the Median. The Analysis of Accuracy of Estimation, Acta Universitatis Lodziensis. Folia Oeconomica, 235, 21–29.

Domański C., Pruska K., (2000), Nieklasyczne metody statystyczne, Polskie Wydawnictwo Ekonomiczne, Warszawa.

Efron B., (1979), Bootstrap Methods: Another Look at the Jackknife, The Annals of Statistics, 7 (1), 1–26.

Evans D. L., Leemis L. M., Drew J. H., (2006), The Distribution of Order Statistics for Discrete Random Variables With Applications of Bootstrapping, Journal on Computing, 18 (1), 19–30.

Fisher N. I., Hall P., (1991), Bootstrap Algorithms for Small Samples, Journal of Statistical Planning and Inference, 27, 157–169.

Hutson A. D., Ernst M. D., (2000), The Exact Bootstrap Mean and Variance of an L-estimator, Journal of the Royal Statistical Society: Series B, 62 (1), 89–94.

Kisielińska J., (2013), The Exact Bootstrap Method Shown on the Example of the Mean and Variance Estimation, Computational Statistics, 28 (3), 1061–1077.

Maritz J. S., Jarrett R. G., (1978), A Note on Estimating the Variance of the Sample Median, Journal of the American Statistical Association, 73 (361), 194–196.

Pekasiewicz D., (2015), Statystyki pozycyjne w procedurach estymacji i ich zastosowania w badaniach ekonomicznych, Wydawnictwo Uniwersytetu Łódzkiego, Łódź.

Pruska K., (2007), Estimation of Bias and Variance of Sample Median by Jackknife and Bootstrap Methods, Acta Universitatis Lodziensis, Folia Oeconomica, 206, 67–78.

Wilcox R. R., (2001), Fundamentals of Modern Statistical Methods, Springer, New York.

Zieliński R., (1995), Estimating Median and Other Quantiles in Nonparametric Models, Applicationes Mathematicae, 23 (3), 363–370.

Back to top
Copyright © 2019 Statistics Poland