Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-12T04:18:43.088Z Has data issue: false hasContentIssue false
  • English
  • Français

TESTING HYPOTHESES ABOUT ABSOLUTE CONCENTRATION CURVES AND MARGINAL CONDITIONAL STOCHASTIC DOMINANCE

Published online by Cambridge University Press:  22 April 2008

Edna Schechtman ,
Amit Shelef ,
Shlomo Yitzhaki  and
Ričardas Zitikis
Edna Schechtman*
Affiliation:
Ben-Gurion University of the Negev
Amit Shelef
Affiliation:
Ben-Gurion University of the Negev
Shlomo Yitzhaki
Affiliation:
The Hebrew University of Jerusalem and Central Bureau of Statistics
Ričardas Zitikis
Affiliation:
University of Western Ontario
*
Address correspondence to Edna Schechtman, Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider statistical tests concerning various relationships between two absolute concentration curves (ACCs). In particular, we consider tests for determining if the two ACCs coincide, if one is above another in a specified order, or if they do not intersect without specifying which one is above/below the other one. These problems are of interest in the context of marginal conditional stochastic dominance (MCSD). Constructing statistical tests for the MCSD relies on ideas and also on their modifications developed by Linton, Maasoumi, and Whang (2005, Review of Economic Studies 72, 735–765) in the context of stochastic dominance for distribution functions. Our theoretical considerations are supplemented with a simulation study.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 1044 - 1062
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barrett, G.F. ’ Donald, S.G. (2003) Consistent tests for stochastic dominance. Econometrica 71, 71–104.CrossRefGoogle Scholar
Bodurtha, J.N. (2006) Dominated Portfolios and Efficient Portfolio Reallocation for General Discrete Distributions and all Risk-Averse Investors. Manuscript, McDonough School of Business, Georgetown University.Google Scholar
Chow, K.V. (2001) Marginal conditional stochastic dominance, statistical inference and measuring portfolio performance. Journal of Financial Research 24, 289–307.CrossRefGoogle Scholar
Davidson, R. ’ Duclos, J.-Y. (2000) Statistical inference for stochastic dominance and for the measurement of poverty and inequality. Econometrica 68, 1435–1464.Google Scholar
Davydov, Y. ’ Egorov, V. (2000) Functional limit theorems for induced order statistics. Mathematical Methods of Statistics 9, 297–313.Google Scholar
Eubank, R., Schechtman, E., ’ Yitzhaki, S. (1993) A test for second order stochastic dominance. Communications in Statistics—Theory and Methods 22, 1893–1905.Google Scholar
Horváth, L., Kokoszka, P., ’ Zitikis, R. (2006) Testing for stochastic dominance using the weighted McFadden-type statistic. Journal of Econometrics 133, 191–205.CrossRefGoogle Scholar
Kuosmanen, T. (2004) Efficient diversification according to stochastic dominance criteria. Management Science 50, 1390–1406.CrossRefGoogle Scholar
Linton, O., Maasoumi, E., ’ Whang, Y.J. (2005) Consistent testing for stochastic dominance under general sampling schemes. Review of Economic Studies 72, 735–765.Google Scholar
Lundin, D. (2001) Welfare-improving carbon dioxide tax reform taking externality and location into account. International Tax and Public Finance 8, 815–835.Google Scholar
Mayshar, J. ’ Yitzhaki, S. (1995) Dalton-improving indirect tax reform. American Economic Review 85, 793–807.Google Scholar
Post, T. (2003) Empirical tests for stochastic dominance efficiency. Journal of Finance 58, 1905–1931.Google Scholar
Rao, C.R. ’ Zhao, L.C. (1995) Convergence theorems for empirical cumulative quantile regression functions. Mathematical Methods of Statistics 4, 81–91.Google Scholar
Schechtman, E. ’ Shalit, H. (2006) Testing the Necessary Conditions for the Marginal Conditional Stochastic Dominance. Manuscript, Ben-Gurion University of the Negev.Google Scholar
Schechtman, E. ’ Zitikis, R. (2006) Gini indices as areas and covariances: What is the difference between the two representations? Metron 54, 385–397.Google Scholar
Seiler, E.J. (2001) A nonparametric test for marginal conditional stochastic dominance. Applied Financial Economics 11, 173–177.Google Scholar
Sen, A. (1997) On Economic Inequality. Expanded edition with a substantial annex by J.E. Foster ’ A. Sen. Oxford University Press.Google Scholar
Shalit, H. ’ Yitzhaki, S. (1994) Marginal conditional stochastic dominance. Management Science 40, 670–684.Google Scholar
Shalit, H. ’ Yitzhaki, S. (2003) Solving the portfolio allocation puzzle, a note. American Economic Review 93, 1002–1008.Google Scholar
Shelef, A. (2006) Constructing a statistical test for the optimality of portfolios. M.Sc. thesis, Department of Industrial Engineering and Management, Ben-Gurion University of the Negev.Google Scholar
Shorrocks, A.F. (1983) Ranking income distributions. Economica 50, 3–17.CrossRefGoogle Scholar
Yitzhaki, S. (1990) On the sensitivity of a regression coefficient to monotonic transformations. Econometric Theory 6, 165–169.Google Scholar
Yitzhaki, S. ’ Mayshar, J. (1997) Characterizing Efficient Portfolios. Manuscript. Department of Economics, Hebrew University.Google Scholar
Yitzhaki, S. ’ Schechtman, E. (2004) The Gini instrumental variables, or “the double IV estimator.” Metron 52, 1–27.Google Scholar