Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

A New Approach to Importance Sampling in Taylor’s Stochastic Volatility Model

This article presents the general analysis of finite high-dimensional integrals using the Importance Sampling (IS) in aim to the parameter estimation of Taylor’s stochastic volatility (SV) model. After we proceed to make an alternative derivation for Sequential Importance Sampling (SIS) in previous literatures, we propose a new approach to select the optimal parameters of sampler, which is called as Universal Importance Sampling (UIS). UIS minimizes the Monte Carlo variance and numerically performs at least the same accurately as the SIS algorithm, but the computational efficiency get greatly improved. We apply both methods and investigate the SV model on the data, then make comparisons of the results.     

Effects of censoring on the robustness of exponential-based confidence intervals for median lifetime

Statistical procedures for constructing confidence intervals for median lifetime often rest on a distributional assumption for failure times.This paper explores the interplay between censoring levels and robustness for two construction procedures based on exponential lifetime, subject to general right-censoring. Data are simulated from nearby Weibull distributions. As expected, the simulations indicate that when the exponential assumption is not satisfied, observed coverage by the confidence intervals may differ substantially from the specified coverage level. The marked improvement in the robustness properties of the intervals as the level of censoring increases suggests questions for future research.     

On the asymptotic properties of parameter estimates in a regression model with non-normally distributed errors

As pointed out in a recent paper by Amirkhalkhali and Rao (1986) (henceforth referred to as A&R), the usual assumption of normality for the error terms of a regression model isoften untenable. However, when this assumption is dropped, it may be difficult to characterize parameter estimates for the model. For example, A&R (p. 189) state that “if the regression errors are non-normal, we are not even sure of their [e.g., the generalized least squares parameter estimates1] asymptotic properties.” A partial answer, however, is given by Spall and Wall (1984), which presents an asymptotic distribution theory for Kalman filter estimates for cases where the random terms of the state space model are not necessarily Gaussian. Certain of these asymptotic distribution results are also discussed in Spall (1985) in the context of model validation (diagnostic checking)     

Bayesian Risk Ratio Analysis

The classical confidence interval approach has failed to find exact intervals, or even a consensus on the best approximate intervals, for the ratio of two binomial probabilities, the so-called risk ratio. The problem is reexamined from a Bayesian viewpoint, and a simple graphical presentation of the risk ratio assessment is given in such a way that sensitivity to the selected prior distribution can be readily examined.     

Statistical Computing: History and Trends

The evolution of computers is currently in a period of rapid change, stimulated by radically cheaper and smaller devices for processing and memory. These changes are certain to provide major opportunities and challenges for the use of computers in statistics. This article looks at history and current trends, in both general computing and statistical computing, with the goal of identifying key features and requirements for the near future. A discussion of the S language developed at Bell Laboratories illustrates some program design principles that can make future work on statistical programs more effective and more valuable.