Some almost sure representations are obtained for the TJW product-limit estimator of a distribution function when the data are subject to random left-truncation and right-censorship. These results extend the theorems of Stute (1993) which were obtained for purely truncated data.

In this paper an asymptotic distribution is obtained for the maximal deviation between the kernel density estimator and the density when the data are subject to random left truncation and right censorship. Based on this result we propose a fully sequential procedure for constructing a...

Comparison of two samples can sometimes be conducted on the basis of analysis of receiver operating characteristic (ROC) curves. A variety of methods of point estimation and confidence intervals for ROC curves have been proposed and well studied. We develop smoothed empirical likelihood-based...

In this paper we consider the TJW product-limit estimatorFn(x) of an unknown distribution functionFwhen the data are subject to random left truncation and right censorship. An almost sure representation of PL-estimatorFn(x) is derived with an improved error bound under some weaker assumptions....

In this paper we develop wavelet methods for detecting and estimating jumps and cusps in the mean function of a non-parametric regression model. An important characteristic of the model considered here is that it allows for conditional heteroscedastic variance, a feature frequently encountered...

To compare two samples of censored data, we propose a unified method of semi-parametric inference for the parameter of interest when the model for one sample is parametric and that for the other is nonparametric. The parameter of interest may represent, for example, a comparison of means, or...

This edited volume expands the scope of risk management beyond finance to include resources and environment issues in China. It presents the state-of-the-art approaches of using risk management to effectively manage resources and environment. Both case studies and theoretical methodologies are...