×

The asymptotics of the least trimmed absolute deviations (LTAD) estimator. (English) Zbl 0797.62029

This paper studied the least trimmed absolute deviations (LTAD) estimator of location. The LTAD estimator is defined by minimizing the least sum of absolute deviations on all possible half-samples. Consistency and asymptotic normality of the LTAD are derived. A comparison of asymptotic variances of the LTAD, Rousseeuw’s least median of squares (LMS) and LTS are carried out.

MSC:

62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Butler, R. W., Nonparametric interval and point prediction using data trimmed by a Grubbs-type outlier rule, Ann. Statist., 10, 197-204 (1982) · Zbl 0487.62040
[2] Butler, R. W.; Davies, P. L.; Jhun, M., Asymptotics of the minimum covariance determinate estimator, Ann., Statist. (1994), to appear in
[3] Hampel, F. R.; Ronchetti, E. M.; Rousseeuw, P. J.; Stahel, W., Robust Statistics: The Approach Based on Influence Functions (1986), Wiley: Wiley New York · Zbl 0593.62027
[4] Hettmansperger, T. P.; Sheather, S. J., A cautionary note on the method of least median squares, Amer. Statist., 46, 79-83 (1992)
[5] Hössjer, O., Rank-based estimates in the linear model with high breakdown point, Ph.d. thesis (1991), Dept. of Math. Uppsala Univ: Dept. of Math. Uppsala Univ Uppsala, Sweden, Report 1991:5
[6] Niinimaa, A.; Oja, H.; Tableman, M., The finite-sample breakdown point of the Oja bivariate median and the corresponding half-samples version, Statist. Probab. Lett., 1, 325-328 (1990) · Zbl 0712.62046
[7] Oja, H., Descriptive statistics for multivariate distributions, Statist. Probab. Lett., 1, 327-332 (1983) · Zbl 0517.62051
[8] Parzen, E., Nonparametric statistical data modeling, J. Amer. Statist. Assoc., 74, 105-131 (1979) · Zbl 0407.62001
[9] Rousseeuw, P. J., Multivariate estimation with high breakdown point, (Mathematical Statistics and Applications, B (1985), Reidel: Reidel Dordrecht), 283-297
[10] Rousseeuw, P. J.; Leroy, A. M., Robust Regression and Outlier Detection (1987), Wiley: Wiley New York
[11] Serling, R. A., Approximation Theorems in Mathematical Statistics (1980), Wiley: Wiley New York
[12] Tableman, M., The influence functions for the least trimmed squares and the least trimmed absolute deviations, Statist. Probab. Lett., 19, 329-337 (1994) · Zbl 0803.62027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.