This paper develops a sampling algorithm for bandwidth estimation in a nonparametric regression model with continuous and discrete regressors under an unknown error density. The error density is approximated by the kernel density estimator of the unobserved errors, while the regression function is estimated using the Nadaraya-Watson estimator admitting continuous and discrete regressors. We derive an approximate likelihood and posterior for bandwidth parameters, followed by a sampling algorithm. Simulation results show that the proposed approach typically leads to better accuracy of the resulting estimates than cross-validation, particularly for smaller sample sizes. This bandwidth estimation approach is applied to nonparametric regression model of the Australian All Ordinaries returns and the kernel density estimation of gross domestic product (GDP) growth rates among the organisation for economic co-operation and development (OECD) and non-OECD countries.

Testing for stochastic dominance between distributions is an important issue in the study of asset distribution, income distribution and market efficiency. This paper applies Monte Carlo simulations to examine the size and power of some commonly used stochastic dominance tests when the underlying distributions are correlated, and either homoskedastic or heteroskedastic. Our Monte Carlo study shows that the test suggested by Davidson and Duclos (2000) has a better size- and power-performance than two alternative tests developed by Kaur, Rao and Singh (1994) and Anderson (1996). In addition, when the underlying distributions are heteroskedastic, both the size and power of test developed by Davidson and Duclos (2000) are still superior to those of the two alternative tests.