Browse > Article
http://dx.doi.org/10.5351/KJAS.2010.23.2.375

A Trimmed Spatial Median Estimator Using Bootstrap Method  

Lee, Dong-Hee (Department of Business Administration, Kyonggi University)
Jung, Byoung-Cheol (Department of Statistics, University of Seoul)
Publication Information
The Korean Journal of Applied Statistics / v.23, no.2, 2010 , pp. 375-382 More about this Journal
Abstract
In this study, we propose a robust estimator of the multivariate location parameter by means of the spatial median based on data trimming which extending trimmed mean in the univariate setup. The trimming quantity of this estimator is determined by the bootstrap method, and its covariance matrix is estimated by using the double bootstrap method. This extends the work of Jhun et al. (1993) to the multivariate case. Monte Carlo study shows that the proposed trimmed spatial median estimator yields better efficiency than a spatial median, while its covariance matrix based on double bootstrap overcomes the under-estimating problem occurred on single bootstrap method.
Keywords
Bootstrap; multivariate location parameter; spatial median; trimming estimation; trimmed spatial median;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Zuo, Y. (2002). Multivariate trimmed means based on data depth, In Statistical Data Analysis Based on the L1-Norm and Related Methods, (ed. by Y. Dodge), 313-322.
2 Brown, B. M. (1983). Statistical uses of the spatial median, Journal of the Royal Statistical Society B, 45, 25-30.
3 Gordaliza , A. (1991). Best approximations to random variables based on trimming procedures, Journal of Approximation Theory, 64, 162-180.   DOI
4 Gower, J. C. (1974). Algorithm AS 78: The mediancentre, Applied Statistics, 23, 466-470.   DOI   ScienceOn
5 Hawkins, D. M., Bradu, D. and Kass, G. V. (1984). Location of several outliers in multiple regression data using elemental sets, Technometrics, 26, 197-208.   DOI
6 Hettmansperger, T. P. and Randles, R. H. (2002). A practical affine equivariant multivariate median, Biometrika, 89, 851-860.   DOI   ScienceOn
7 Jhun, M., Kang, C. W. and Lee, J. C. (1993). Bootstrapping trimmed estimators in statistical inferences, Proceedings of the Asian Conference on Statistical Computing.
8 Masse, J-C. (2004). Asymptotics for the Tukey depth process, with an application to a multivariate trimmed mean, Bernoulli, 10, 379-419.
9 Masse, J-C. (2009). Multivariate trimmed means based on the Tukey depth, Journal of Statistical Planning and Inference, 139, 366-384.   DOI   ScienceOn
10 Masse, J-C. and Plante, J-F. (2003). A Monte Carlo study of the accuracy and robustness of ten bivariate location estimators, Computational Statistics & Data Analysis, 42, 1-26.   DOI   ScienceOn
11 Somorcik, J. (2006). Tests using spatial median, Austrian Journal of Statistics, 35, 331-338.
12 Vandev, D. L. (1995). Computing of trimmed $L_1$ median, In Multidimensional Analysis in Behavioral Sciences. Philosophic to technical, 152-157.
13 소선하, 이동희, 정병철 (2009). 다변량 자료에서 위치모수에 대한 로버스트 검정, <응용통계연구>, 22, 1355-1364.   과학기술학회마을   DOI
14 Arcones, M. A. (1995). Asymptotic normality of multivariate trimmed means, Statistics and Probability Letters, 25, 43-53.   DOI   ScienceOn