Abstract
It is common practice to perform an Exploratory Data Analysis to decide whether to use a classical or a robust test; i.e., to choose between a classical or a robust result. What is not so clear is how to choose among the results provided by different competing robust tests. In this paper we propose to use the function p − value line, that we shall define later, to compare the results obtained by different tests in order to choose one: the result with largest p-value line. This function takes into account the usual trade-off between robustness and power that is present in most, if not all, robust tests, trade-off that is expressed thought a parameter fixed in a subjective way. With our proposal we can fix it in an objective manner. We shall apply this proposal to choose the trimming fraction in the location test based on the trimmed mean.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
García-Pérez, A.: An approximation to the small sample distribution of the trimmed mean (submitted, 2012)
García-Pérez, A.: A linear approximation to the power function of a test. Metrika 76 (2012)
Jing, B., Robinson, J.: Saddlepoint approximations for marginal and conditional probabilities of transformed variables. Ann. Statist. 22(3), 1115–1132 (1994)
Lô, S.N., Ronchetti, E.: Robust and accurate inference for generalized linear models. J. Multivariate Anal. 100(9), 2126–2136 (2009)
R Development Core Team: R: A Language and Environment for Statistical Computing, Vienna, Austria (2011) ISBN 3-900051-07-0, http://www.R-project.org
Robinson, J., Ronchetti, E., Young, G.A.: Saddlepoint approximations and tests based on multivariate m-estimates. Ann. Statist. 31(4), 1154–1169 (2003)
Staudte, R.G., Sheather, S.J.: Robust Estimation and Testing. Wiley Series in Probability and Statistics, vol. 220. John Wiley & Sons, Ltd., New York (1990)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
García-Pérez, A. (2013). The p-value Line: A Way to Choose from Different Test Results. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-33042-1_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33041-4
Online ISBN: 978-3-642-33042-1
eBook Packages: EngineeringEngineering (R0)