Improvements in the power of empirical stochastic dominance comparisons through kernel density estimation: a monte carlo study

Abstract

Difficulties inherent in estimation techniques frequently subvert the theoretical potential of stochastic dominance. Monte Carlo experiments repeatedly demonstrate that sampling errors cause the failure of stochastic dominance in empirical applications which utilize the empirical distribution function as an estimator of the cumulative distribution function. Similar experiments also reveal that nonparametric kernel estimators can significantly improve the success rate. The choice of the degree of smoothing applied by the kernel estimation procedure yields a familiar trade-off similar to statistical Type I and Type II errors in hypothesis testing. In hypothesis testing, a small afavors the null hypothesis at the risk of failing to reject when an alternative is true. Similarly, little or no smoothing encourages acceptance of the null hypothesis of a no dominance conclusion even when the alternative of a dominant relationship between distributions exists in the population. This paper establishes the potential of kernel density estimation to improve the performance of stochastic dominance comparisons of empirical distributions. It also identifies the issue of optimal bandwidth selection as an important direction for future research into this promising methodology.

Keywords:

• Efficiency analysis
• majorization
• nonparametric statistics