Kernel Smoothing to Improve Bootstrap Confidence Intervals

Some studies of the bootstrap have assessed the effect of smoothing the estimated distribution that is resampled, a process usually known as the smoothed bootstrap. Generally, the smoothed distribution for resampling is a kernel estimate and is often rescaled to retain certain characteristics of the empirical distribution. Typically the effect of such smoothing has been measured in terms of the mean-squared error of bootstrap point estimates. The reports of these previous investigations have not been encouraging about the efficacy of smoothing. In this paper the effect of resampling a kernel-smoothed distribution is evaluated through expansions for the coverage of bootstrap percentile confidence intervals. It is shown that, under the smooth function model, proper bandwidth selection can accomplish a first-order correction for the one-sided percentile method. With the objective of reducing the coverage error the appropriate bandwidth for one-sided intervals converges at a rate of n ^−1/4, rather than the familiar n ^−1/5 for kernel density estimation. Applications of this same approach to bootstrap t and two-sided intervals yield optimal bandwidths of order n ^−1/2. These bandwidths depend on moments of the smooth function model and not on derivatives of the underlying density of the data. The relationship of this smoothing method to both the accelerated bias correction and the bootstrap t methods provides some insight into the connections between three quite distinct approximate confidence intervals.     

The impact of missing values in the concentration–time curve on the assessment of bioequivalence

A complication that may arise in some bioequivalence studies is that of ‘incomplete subject profiles’, caused by missing values that occur at one or more sampling points in the concentration–time curve for some study subjects. We assess the impact of incomplete subject profiles on the assessment of bioequivalence in a standard two‐period crossover design. The specific aim of the investigation is to assess the impact of four different patterns of missing concentration values on the coverage level of a 90% nominal two‐sided confidence interval for the ratio of geometric means and then to consider the impact on the probability of concluding bioequivalence. An overall conclusion from the results is that random missingness – that is, missingness for reasons unrelated to the bioavailability of the formulation involved or, more generally, to any aspect of the study design and conduct – has a damaging effect on the study conclusions only when the number of missing values is fairly large. On the other hand, a missingness pattern that potentially has a very damaging effect on the study conclusions is that which arises when values are missing ‘late’ in the concentration–time curve. Copyright © 2005 John Wiley & Sons, Ltd     

浅谈班主任工作

为促进班集体建设,班主任要树立正确的班集体发展目标,建立健全班集体组织结构,把德育放在教育首位,以培养学生学习能力,端正其学习态度为工作重心,并结合本校特点,加强爱心教育.     

从世界零售业发展看中国零售业态发展走势

零售业是一个国家经济的重要组成部分。发达国家零售业不断出现新的经营方式和销售方式 ,并代表着未来零售业的发展方向。借鉴发达国家零售业发展经验 ,遵循发展规律 ,对正确把握我国零售业态发展方向 ,使中国零售业不断发展壮大 ,具有重要意义。     

一种高性能APD反向偏压控制电路的实现

本文设计了一种应用于APD反向偏压控制的DC/DC变换电路,并对实测结果进行了分析。     

五四时期统一战线的组成和发展

五四运动中的统一战线是中国新民主主义革命统一战线的开端 ,它是由新文化运动统一战线和爱国运动统一战线所组成的 ,范围是极其广泛的 ,是在矛盾运动中向前发展的     

Dose finding with continuous outcome in phase I oncology trials

The goal of a phase I clinical trial in oncology is to find a dose with acceptable dose‐limiting toxicity rate. Often, when a cytostatic drug is investigated or when the maximum tolerated dose is defined using a toxicity score, the main endpoint in a phase I trial is continuous. We propose a new method to use in a dose‐finding trial with continuous endpoints. The new method selects the right dose on par with other methods and provides more flexibility in assigning patients to doses in the course of the trial when the rate of accrual is fast relative to the follow‐up time. Copyright © 2014 John Wiley & Sons, Ltd.     

A Model for Water Pricing

This note describes a situation in which a simple mathematical model helped solve an important practical problem: how to price water fairly. It is intended as an example, rather than as a mathematical contribution to control theory.     

On the adequacy of the chi-squared approximation for the coefficient of variation

The X² approximation to the distribution of the sample coefficient of variation of a normally distributed random variable, due to McKay 1932 is not nearly as accurate as suggested by the confirmatory studies of Fieller 1932 and Pearson 1932.The approximation will, however, be adequate in many practical situations and has the convenience of requiring nothing more than the readily available tables of x².     

On the Breakdown Properties of Some Multivariate M‐Functionals*

Abstract. For probability distributions on ? ^q, a detailed study of the breakdown properties of some multivariate M‐functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution‐free’ M‐functional of scatter is given. These include a symmetrized version of Tyler's M‐functional of scatter, and the multivariate t M‐functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M‐functional of scatter and of its symmetrized version are 1/q and , respectively. For the multivariate t M‐functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/( q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low‐dimensional subspaces.