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Title: Test statistics for prospect and Markowitz stochastic dominances with applications
Authors: Bai, Z.
Li, H.
Liu, H. 
Wong, W.-K.
Keywords: Hypothesis testing
Markowitz stochastic dominance
Prospect stochastic dominance
Risk averse
Risk seeking
RS-shaped utility function
S-shaped utility function
Test statistics
Issue Date: Jul-2011
Citation: Bai, Z., Li, H., Liu, H., Wong, W.-K. (2011-07). Test statistics for prospect and Markowitz stochastic dominances with applications. Econometrics Journal 14 (2) : 278-303. ScholarBank@NUS Repository.
Abstract: Levy and Levy (2002, 2004) extend the stochastic dominance (SD) theory for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with S-shaped and reverse S-shaped (RS-shaped) utility functions, respectively. Davidson and Duclos (2000) develop SD tests for risk averters whereas Sriboonchitra et al. (2009) modify their statistics to obtain SD tests for risk seekers. In this paper, we extend their work by developing new statistics for both PSD and MSD of the first three orders. These statistics provide a tool to examine the preferences of investors with S-shaped utility functions proposed by Kahneman and Tversky (1979) in their prospect theory and investors with RS-shaped investors proposed by Markowitz (1952a). We also derive the limiting distributions of the test statistics to be stochastic processes. In addition, we propose a bootstrap method to decide the critical points of the tests and prove the consistency of the bootstrap tests. To illustrate the applicability of our proposed statistics, we apply them to study the preferences of investors with the corresponding S-shaped and RS-shaped utility functionsvis-à-visreturns on iShares andvis-à-visreturns of traditional stocks and Internet stocks before and after the Internet bubble. © 2011 The Author(s). The Econometrics Journal © 2011 Royal Economic Society.
Source Title: Econometrics Journal
ISSN: 13684221
DOI: 10.1111/j.1368-423X.2011.00348.x
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