Interval Estimation for the Difference of Two Independent Variances

Analytical methods for interval estimation of differences between variances have not been described. A simple analytical method is given for interval estimation of the difference between variances of two independent samples. It is shown, using simulations, that confidence intervals generated with this method have close to nominal coverage even when sample sizes are small and unequal and observations are highly skewed and leptokurtic, provided the difference in variances is not very large. The method is also adapted for testing the hypothesis of no difference between variances. The test is robust but slightly less powerful than Bonett's test with small samples.     

On the efficiency of nonparametric variance estimation in sequential dose-finding

Dose-finding in clinical studies is typically formulated as a quantile estimation problem, for which a correct specification of the variance function of the outcomes is important. This is especially true for sequential study where the variance assumption directly involves in the generation of the design points and hence sensitivity analysis may not be performed after the data are collected. In this light, there is a strong reason for avoiding parametric assumptions on the variance function, although this may incur efficiency loss. In this paper, we investigate how much information one may retrieve by making additional parametric assumptions on the variance in the context of a sequential least squares recursion. By asymptotic comparison, we demonstrate that assuming homoscedasticity achieves only a modest efficiency gain when compared to nonparametric variance estimation: when homoscedasticity in truth holds, the latter is at worst 88% as efficient as the former in the limiting case, and often achieves well over 90% efficiency for most practical situations. Extensive simulation studies concur with this observation under a wide range of scenarios.     

Statistical inference in the partial linear models with the inverse gaussian kernel

Symmetric kernel smoothing is commonly used in estimating the nonparametric component in the partial linear regression models. In this article, we propose a new estimation method for the partial linear regression models using the inverse Gaussian kernel when the explanatory variable of the nonparametric component is non-negatively supported. As an asymmetric kernel function, the inverse Gaussian kernel is also supported on the non-negative half line. The asymptotic properties, including the asymptotic normality, uniform almost sure convergence, and the iterated logarithm laws, of the proposed estimators are thoroughly discussed for both homoscedastic and heteroscedastic cases. The simulation study is conducted to evaluate the finite sample performance of the proposed estimators.