Advanced SearchSearch Tips
A Trimmed Spatial Median Estimator Using Bootstrap Method
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A Trimmed Spatial Median Estimator Using Bootstrap Method
Lee, Dong-Hee; Jung, Byoung-Cheol;
  PDF(new window)
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.
Bootstrap;multivariate location parameter;spatial median;trimming estimation;trimmed spatial median;
 Cited by
분할표 분석을 위한 절사 LAD 추정량과 최적 절사율 결정,최현집;

응용통계연구, 2010. vol.23. 6, pp.1235-1243 crossref(new window)
소선하, 이동희, 정병철 (2009). 다변량 자료에서 위치모수에 대한 로버스트 검정, <응용통계연구>, 22, 1355-1364. crossref(new window)

Arcones, M. A. (1995). Asymptotic normality of multivariate trimmed means, Statistics and Probability Letters, 25, 43-53. crossref(new window)

Brown, B. M. (1983). Statistical uses of the spatial median, Journal of the Royal Statistical Society B, 45, 25-30.

Gordaliza , A. (1991). Best approximations to random variables based on trimming procedures, Journal of Approximation Theory, 64, 162-180. crossref(new window)

Gower, J. C. (1974). Algorithm AS 78: The mediancentre, Applied Statistics, 23, 466-470. crossref(new window)

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. crossref(new window)

Hettmansperger, T. P. and Randles, R. H. (2002). A practical affine equivariant multivariate median, Biometrika, 89, 851-860. crossref(new window)

Jhun, M., Kang, C. W. and Lee, J. C. (1993). Bootstrapping trimmed estimators in statistical inferences, Proceedings of the Asian Conference on Statistical Computing.

Masse, J-C. (2004). Asymptotics for the Tukey depth process, with an application to a multivariate trimmed mean, Bernoulli, 10, 379-419.

Masse, J-C. (2009). Multivariate trimmed means based on the Tukey depth, Journal of Statistical Planning and Inference, 139, 366-384. crossref(new window)

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. crossref(new window)

Somorcik, J. (2006). Tests using spatial median, Austrian Journal of Statistics, 35, 331-338.

Vandev, D. L. (1995). Computing of trimmed $L_1$ median, In Multidimensional Analysis in Behavioral Sciences. Philosophic to technical, 152-157.

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.