This paper studies an alternative bias correction for the M-estimator, which is obtained by correcting the moment equation in the spirit of Firth (1993). In particular, this paper compares the stochastic expansions of the analytically bias-corrected estimator and the alternative estimator and...

This paper studies the uniform convergence rate of the turncated SNP (semi-nonparametric) density estimator. Using the uniform convergence rate result we obtain, we propose a test statistic testing the equivalence of two unknown densities where two densities are estimated using the SNP estimator...