# BOOTSTRAPPING CERTAIN MEASURES OF LOCATION

## Keywords:

Relative Efficiency, Winsorized Mean, Median, Trimmed Mean, Bootstrap Standard Error## Abstract

The focus of this paper is on consistent estimates of the standard error of certain measures of location. The bootstrap approach was adopted to compute the standard error for assessing the relative efficiencies of some measures of location. The R statistical package was employed to obtain data from some distributions and real data for the analysis. Employing the re-sampling procedure inherent in bootstrapping, it was established analytically that bootstrap standard errors are smaller for the median estimator than their counterpart. The median was found to be the most robust since it produces the least bootstrap standard error and relative efficiency of less than one when compared to the other estimators under study. However, the mean was the most efficient compared to the other measures of the location under study when the distribution is normally distributed.

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## References

Efron, B. (1979). Bootstrap methods: Annals of Statistics 7, 1-26.

.Efron, B. and Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman &Hall. U.S.A.

. Özdemir, A.F. (2010). Comparing measures of location when the underlying distribution has heavier tails than normal. statistikçilerDergisi 3,8-16

. Liu, R. Y. (1988). Bootstrap Procedures under Some Non-i.i.d Models. Annals of Statistics. Vol.18, No. 4, 1696- 1708

. Yildiztepe, E. (2020). Comparison of Conventional, Balanced and Sufficient Bootstrapping Approaches via Confidence Intervals and Efficiency. Mugla Journal of Science and Technology, 6(2), 111-120.

. Breiman, P. (1996). On Robust Estimation. Annals of Statistics, 9. 1196 - 1217.

. Hamadu, D. (2012). A Bootstrap Approach to Robust Regression. International Journal of Applied Science and Technology. Vol. 2 No. 9.

. Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing. Elsevier Academic Press, Third Edition. New York.

. Andersen, R. (2012). Modern methods for robust regression. University of Toronto. Sage University Paper Series. Canada.

. Kenney, J.F and Keeping, E. S. (1962). Mathematics of Statistics. Part 2, Second edition, Van Nostrand. University of Michigan, U.S.A.

. McKean, J.W and Schrader, R.M. (1984). Geometry of Robust Procedures in Linear Models. Journal of Royal Statistical Society. Series B (Methodological) Wiley: Vol. 42, No.3, 366-371

. Wilcox, R. R. (2005). Introduction to Robust Estimation and Hypothesis Testing. Elsevier Academic Pres, Second Edition. New York.

. Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. Oxford University Press.

. Wilcox, R. R and Keselman, H. J. (2003). Modern Robust Data Analysis Methods: Measures of Central Tendency. Psychological Methods, 8(3), 254-274.

. Dixon, W.J and Tukey, J.W. (1968). Approximate Behaviour of the Distribution of Winsorized (Trimming/Winsorization). American Statistical Association and American Society for Quality. Vol. 10, No 1, 83- 98.

. Furness, R.W., and Birkhead, T.R. (1984). Seabird colony distributions suggest for food supplies during the breeding season. Nature, 311, 655-656.

. Hamilton, L.C. (1992). Regression with Graphics- Second Course in Applied Statistics. Brooks/Cole Publishing Company. Belmot, California.

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*The Journals of the Nigerian Association of Mathematical Physics*,

*65*, 95 – 102. https://nampjournals.org.ng/index.php/home/article/view/37