Abstract
In this paper we construct estimators for the parameters of the multivariate sinh-1-normal distribution. We discuss some properties of these estimators, such as consistency, B-robustness and asymptotic normality.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. J. Conover and R. L. Iman, The Rank Transformation as a Method of Discrimination with Some Examples. Comm. Statist. Theory Methods 5 (1980), 465–487.
C. Croux and G. Haesbroeck, Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies. Biometrika 87 (2000), 603–618.
P. L. Davies, Asymptotic Behavior of S-estimators of Multivariate Location Parameters and Dispersion Matrices. Ann. Statist. 15 (1987), 1269–1292.
F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel, Robust Statistics: the Approach Based on Influence Function. Wiley, New York, 1986.
M. E. Johnson, Multivariate Statistical Simulation. Wiley, New York, 1987.
N. L. Johnson, System of Frequency Curves Generated by Methods of Translation. Biometrika 36 (1949), 149–176.
S. L. Koffler and D. A. Penfield, Nonparametric Discrimination Procedures for Non-normal Distributions. J. Statist. Comput. Simulation 8 (1979), 281–299.
P. A. Lachenbruch, C. Sneeringer, and L. T. Revo, Robustness of the Linear and Quadratic Discriminant Function to Certain Types of Non-Normality. Comm. Statist. Theory Methods 1 (1973), 39–56.
K. V. Mardia, J. T. Kent, and J. M. Bibby, Multivariate Analysis. Academic Press, 1994.
R. A. Maronna, Robust M-estimators of Multivariate Location and Scatter. Ann. Statist. 4 (1976), 51–67.
R. A. Maronna and V. Yohai, Robust Estimation of Multivariate Location and Scatter. In S. Kots, C. Read, and D. Banks, editors, Encyclopedia of Statistical Sciences. Wiley, 1998.
P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection. Wiley, 1987.
D. Ruppert, Computing S-estimators for Regression and Multivariate Location/ Dispersion. J. Comput. Graph. Statist. 1 (1992), 253–270.
A. Toma, Robust Estimators for the Parameters of Multivariate Lognormal Distributions. Comm. Statist. Theory Methods 32 (2003), 1405–1417.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Basel AG
About this paper
Cite this paper
Toma, A. (2004). Robust Estimations for Multivariate Sinh-1-Normal Distribution. In: Hubert, M., Pison, G., Struyf, A., Van Aelst, S. (eds) Theory and Applications of Recent Robust Methods. Statistics for Industry and Technology. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7958-3_31
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7958-3_31
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9636-8
Online ISBN: 978-3-0348-7958-3
eBook Packages: Springer Book Archive