Nonparametric tests for stochastic ordering
We present two new tests for stochastic ordering in a standard two-sample scheme. We approach the problem via its reparametrization in terms of Fourier coefficients in some corresponding system of functions and combining the resulting empirical Fourier coefficients. The empirical Fourier coefficients can be seen to be the asymptotically optimal linear rank statistics for the local sequences of nonparametric alternatives related to the introduced system of functions. Therefore, our first construction of the test is via multiple testing. The second test is based on sum of squares of censored empirical Fourier coefficients with the number of summands determined via a new model selection rule. The selection rule is fully automatic. Extensive simulations show that the new solutions improve upon existing tests based on adjusted variants of classical Kolmogorov–Smirnov, Anderson–Darling and L 1 -distance-based statistics, among others. We show that both tests control the error of the first kind for any fixed sample sizes and are capable of detecting essentially any alternative as the sample sizes are growing to infinity. We also discuss several aspects of our constructions, including possible efficiency calculations and asymptotic comparisons. Copyright Sociedad de Estadística e Investigación Operativa 2012
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 21 (2012)
Issue (Month): 4 (December)
|Contact details of provider:|| Web page: http://www.springerlink.com/link.asp?id=120411|
|Order Information:||Web: http://link.springer.de/orders.htm|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
- Escanciano, Juan Carlos & Mayoral, Silvia, 2010.
"Data-driven smooth tests for the martingale difference hypothesis,"
Computational Statistics & Data Analysis,
Elsevier, vol. 54(8), pages 1983-1998, August.
- Juan Carlos Escanciano & Silvia Mayoral, . "Data-Driven Smooth Tests for the Martingale Difference Hypothesis," Faculty Working Papers 01/07, School of Economics and Business Administration, University of Navarra.
- R. L. Eubank, 2000. "Testing for No Effect by Cosine Series Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 747-763.
- Davidson, R. & Duclos, J.-Y., 1998.
"Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality,"
98a14, Universite Aix-Marseille III.
- Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
- Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
- Christensen, Ronald & Sun, Siu Kei, 2010. "Alternative Goodness-of-Fit Tests for Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 291-301.
- Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
- Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
- Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:730-756. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)or (Christopher F Baum)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.