Consistent Testing for Stochastic Dominance under General Sampling Schemes

Abstract

We propose a procedure for estimating the critical values of the extended Kolmogorov-Smirnov tests of Stochastic Dominance of arbitrary order in the general K-prospect case. We allow for the observations to be serially dependent and, for the first time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent and powerful against some N -½ local alternatives. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably. We describe an alternative method for obtaining critical values based on recentring the test statistic and using full sample bootstrap methods. We compare the two methods in theory and in practice.

Modelling and forecasting multivariate realized volatility

“…The literature on stochastic dominance tests is separated into two groups: one group (McFadden (1989), Klekan, McFadden, and McFadden (1991), Barett and Donald (2003), Linton, Maasoumi, and Whang (2005)) tests the null hypothesis of dominance (H 0 : A 2 B) against the alternative of non-dominance (H 1 : A 2 B), while the other group (Kaur, Rao, and Singh (1994), Davidson and Duclos (2000)) tests the null hypothesis of non-dominance, against the alternative hypothesis of dominance. Most of these tests are developed on the assumptions of i.i.d.…”

“…and cross-independent observations. Due to the fact that we deal with serially (due to GARCH effects) and cross-dependent portfolio returns, we apply here two tests which account for these features: the Linton, Maasoumi, and Whang (2005) (LMW) test and Kaur, Rao, and Singh (1994) (KRS) test. We use the LMW test with the subsampling procedure (Sub) of Politis and Romano (1994a) and Politis, Romano, and Wolf (1999) and the stationary bootstrap (SB) procedure of Politis and Romano (1994b) to obtain consistent critical values for the test.…”

Does faith move stock markets? Evidence from Saudi Arabia

“…Under suitable regularity conditions Linton et al (2005) show thatΛ converges to a functional of a Gaussian process. However, the asymptotic null distribution ofΛ depends on the unknown population distributions, therefore in order to estimate the asymptotic p-values of the test we use the overlapping moving block bootstrap method.…”

Measuring Advances in Equality of Opportunity: The Changing Gender Gap in Educational Attainment in Canada in the Last Half Century

“…Firstly, table 2 examines whether through the 5 decades, children of each parental educational group were made unambiguously worse off or otherwise by employing stochastic dominance tests as prescribed by Linton et al (2005) and Dardanoni and Forcina (1998). With the exception of a few 70s versus 50s comparisons amongst parents with some college and technical education where no dominance relationship was registered, each parental educational group for each cohort stochastically dominated its preceding cohort unanimously, so improvements in educational outcomes were more or less ubiquitous as expected.…”