A Parametric Bootstrap Test for Two-Way ANOVA Model Without Interaction Under Heteroscedasticity

In this article we consider the two-way ANOVA model without interaction under heteroscedasticity. For the problem of testing equal effects of factors, we propose a parametric bootstrap (PB) approach and compare it with existing the generalized F (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the GF test. The PB test performs very satisfactorily even for small samples while the GF test exhibits poor Type I error properties when the number of factorial combinations or treatments goes up. It is also noted that the same tests can be used to test the significance of random effect variance component in a two-way mixed-effects model under unequal error variances.     

On optimising the estimation of high quantiles of a probability distribution

One of the major aims of one-dimensional extreme-value theory is to estimate quantiles outside the sample or at the boundary of the sample. The underlying idea of any method to do this is to estimate a quantile well inside the sample but near the boundary and then to shift it somehow to the right place. The choice of this “anchor quantile” plays a major role in the accuracy of the method. We present a bootstrap method to achieve the optimal choice of sample fraction in the estimation of either high quantile or endpoint estimation which extends earlier results by Hall and Weissman (1997) in the case of high quantile estimation. We give detailed results for the estimators used by Dekkers et al. (1989). An alternative way of attacking problems like this one is given in a paper by Drees and Kaufmann (1998).     

Bootstrap confidence interval estimates of cpk: an introduction

The interpretation of C_pk:, a common measure of process capability and confidence limits for it, is based on the assumption that the process is normally distributed. The non-parametric but computer intensive method called Bootstrap is introduced and three Bootstrap confidence interval estimates for C^ are defined. An initial simulation of two processes (one normal and the other highly skewed) is presented and discussed     

Bounding the resampling risk for sequential Monte Carlo implementation of hypothesis tests

Sequential designs can be used to save computation time in implementing Monte Carlo hypothesis tests. The motivation is to stop resampling if the early resamples provide enough information on the significance of the p-value of the original Monte Carlo test. In this paper, we consider a sequential design called the B-value design proposed by Lan and Wittes and construct the sequential design bounding the resampling risk, the probability that the accept/reject decision is different from the decision from complete enumeration. For the B-value design whose exact implementation can be done by using the algorithm proposed in Fay, Kim and Hachey, we first compare the expected resample size for different designs with comparable resampling risk. We show that the B-value design has considerable savings in expected resample size compared to a fixed resample or simple curtailed design, and comparable expected resample size to the iterative push out design of Fay and Follmann. The B-value design is more practical than the iterative push out design in that it is tractable even for small values of resampling risk, which was a challenge with the iterative push out design. We also propose an approximate B-value design that can be constructed without using a specially developed software and provides analytic insights on the choice of parameter values in constructing the exact B-value design.     

SADDLEPOINT METHODS FOR BOOTSTRAP CONFIDENCE BANDS IN NONPARAMETRIC REGRESSION

Bootstrap techniques have been used to construct confidence bands in nonparametric regression problems (Härdle & Bowman, 1988). Yet the required simulation is generally computationally intensive and therefore makes it difficult to conduct further investigations. In this paper, two saddlepoint methods are considered as alternatives to the naive simulation procedure. Some improvements to Härdle & Bowman's bootstrap method are suggested. The improvements are numerically verified using these efficient and accurate analytic methods.     

Variability in Physical Constant Parameter Values from Standard Data Sources and the Implication of This Variability for Risk Analysis

Physical property values are used in environmental risk assessments to estimate media and risk-based concentrations. However, considerable variability has recently been reported with such values. To evaluate potential variability in physical parameter values supporting a variety of regulatory programs, eight data sources were chosen for evaluation, and chemicals appearing in at least four sources were selected. There were 755 chemicals chosen. In addition, chemicals in seven environmentally important subgroups were also identified for evaluation. Nine parameters were selected for analysis-molecular weight (MolWt), melting point (MeltPt), boiling point (BoilPt), vapor pressure (VP), water solubility (AqSOL), Henry's law constant (HLC), octanol-water partition coefficient (Kow), and diffusion coefficients in air (Dair) and water (Dwater). Results show that while 71% of constituents had equal MolWts across data sources, <3% of the constituents had equivalent parameter values across data sources for AqSOL, VP, or HLC. Considerable dissimilarity between certain sources was also observed. Furthermore, measures of dispersion showed considerable variation in data sets for Kow, VP, AqSOL, and HLC compared to measures for MolWt, MeltPt, BoilPt, or Dwater. The magnitude of the observed variability was also noteworthy. For example, the 95th percentile ratio of maximum/minimum parameter values ranged from 1.0 for MolWt to well over 1.0E + 06 for VP, and HLC. Risk and exposure metrics also varied by similar magnitudes. Results with environmentally important subgroups were similar. These results show that there is considerable variability in physical parameter values from standard sources, and that the observed variability could affect potential risk estimates and perhaps risk management decisions.     

Testing the Martingale Difference Hypothesis

In this paper we consider testing that an economic time series follows a martingale difference process. The martingale difference hypothesis has typically been tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or periodograms. Tests based on these statistics are inconsistent since they cannot detect nonlinear alternatives. In this paper we consider tests that detect linear and nonlinear alternatives. Given that the asymptotic distributions of the considered tests statistics depend on the data generating process, we propose to implement the tests using a modified wild bootstrap procedure. The paper theoretically justifies the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments.     

Development and Consideration of Global Policies for Managing the Future Risks of Poliovirus Outbreaks: Insights and Lessons Learned Through Modeling

The success of the Global Polio Eradication Initiative promises to bring large benefits, including sustained improvements in quality of life (i.e., cases of paralytic disease and deaths avoided) and costs saved from cessation of vaccination. Obtaining and maintaining these benefits requires that policymakers manage the transition from the current massive use of oral poliovirus vaccine (OPV) to a world without OPV and free of the risks of potential future reintroductions of live polioviruses. This article describes the analytical journey that began in 2001 with a retrospective case study on polio risk management and led to development of dynamic integrated risk, economic, and decision analysis tools to inform global policies for managing the risks of polio. This analytical journey has provided several key insights and lessons learned that will be useful to future analysts involved in similar complex decision-making processes.     

The Formation and Development of New Zealand English: Interaction of Gender-Related Variation and Linguistic Change

This research assesses the relative roles played by men and women in the development of New Zealand English. Real-time evidence on the development of NZ English over the past fifty years is provided by comparison of speakers recorded in 1948 and their present day descendants recorded recently. Elements of two vowel shifts are studied, and particular attention is paid to the vowel variables in words such as MOUTH, TRAP and DRESS. Results indicate that women lead in changes which are new and dynamic, but lag behind men in the use of variables representing older changes. While these results mirror patterns of gender-related variation observed in other contexts, explanations in terms of prestige which are often assumed to account for this pattern of variation are found to be inadequate in the New Zealand case. Rather, a hypothesis in terms of dialect contact, and specifically women's preferred discourse strategies in contact situations, is used to explain the process and progress of linguistic change in NZ English.     

李商隐诗作的变异心理分析

李商隐诗作的隐义性历来多难索解。从创作心态角度进行研究 ,前人多侧重于常态心理而未涉及其变异心理。义山诗的变异心理表现为 :担心美好事物易逝的“强迫性感伤”情绪 ,压抑对婚姻的怨恨并将其转化为关爱的“反向形式” ,时有压抑性兴奋并将其雅化诗化为“性诙谐”诗作 ,只有在具禁止色彩的恋爱对象时才燃起“犯禁”的激情并在其影响下形成“忆内”诗与“恋情诗”风格的不同。