Asymptotic and Bootstrap Tests for Infinite Order Stochastic Dominance Via the Method of Empirical Likelihood

2012 ◽  
Author(s):  
Rami Victor Tabri
Keyword(s):  
Empirical Likelihood ◽  
Stochastic Dominance ◽  
Infinite Order ◽  
Order Stochastic Dominance ◽  
Bootstrap Tests

scholarly journals Testing for Restricted Stochastic Dominance: Some Further Results

2009 ◽  
Vol 1 (1) ◽  
pp. 34-59
Author(s):  
Russell Davidson
Keyword(s):  
Stochastic Dominance ◽  
Numerical Algorithms ◽  
Higher Order ◽  
Simulation Experiments ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Nonlinear Optimisation ◽  
Bootstrap Tests ◽  
Asymptotic Tests ◽  
Better Than

Extensions are presented to the results of Davidson and Duclos (2007), whereby the null hypothesis of restricted stochastic non dominance can be tested by both asymptotic and bootstrap tests, the latter having considerably better properties as regards both size and power. In this paper, the methodology is extended to tests of higher-order stochastic dominance. It is seen that, unlike the first-order case, a numerical nonlinear optimisation problem has to be solved in order to construct the bootstrap DGP. Conditions are provided for a solution to exist for this problem, and efficient numerical algorithms are laid out. The empirically important case in which the samples to be compared are correlated is also treated, both for first-order and for higher-order dominance. For all of these extensions, the bootstrap algorithm is presented. Simulation experiments show that the bootstrap tests perform considerably better than asymptotic tests, and yield reliable inference in moderately sized samples.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

scholarly journals The concept of stochastic dominance in ranking investment alternatives

2005 ◽  
Vol 50 (164) ◽  
pp. 135-149
Author(s):  
Dejan Trifunovic
Keyword(s):  
Stochastic Dominance ◽  
Distribution Functions ◽  
Third Order ◽  
Ranking Problem ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Arbitrage Opportunities ◽  
Second Order Stochastic Dominance ◽  
Mean Variance ◽  
Almost Stochastic Dominance

In order to rank investments under uncertainty, the most widely used method is mean variance analysis. Stochastic dominance is an alternative concept which ranks investments by using the whole distribution function. There exist three models: first-order stochastic dominance is used when the distribution functions do not intersect, second-order stochastic dominance is applied to situations where the distribution functions intersect only once, while third-order stochastic dominance solves the ranking problem in the case of double intersection. Almost stochastic dominance is a special model. Finally we show that the existence of arbitrage opportunities implies the existence of stochastic dominance, while the reverse does not hold.

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