Saddlepoint-Based Bootstrap Inference for Quadratic Estimating Equations

Abstract.  We propose an easy to implement method for making small sample parametric inference about the root of an estimating equation expressible as a quadratic form in normal random variables. It is based on saddlepoint approximations to the distribution of the estimating equation whose unique root is a parameter's maximum likelihood estimator (MLE), while substituting conditional MLEs for the remaining (nuisance) parameters. Monotoncity of the estimating equation in its parameter argument enables us to relate these approximations to those for the estimator of interest. The proposed method is equivalent to a parametric bootstrap percentile approach where Monte Carlo simulation is replaced by saddlepoint approximation. It finds applications in many areas of statistics including, nonlinear regression, time series analysis, inference on ratios of regression parameters in linear models and calibration. We demonstrate the method in the context of some classical examples from nonlinear regression models and ratios of regression parameter problems. Simulation results for these show that the proposed method, apart from being generally easier to implement, yields confidence intervals with lengths and coverage probabilities that compare favourably with those obtained from several competing methods proposed in the literature over the past half-century.     

中美石油安全水平对经济增长影响的对比研究——基于灰色关联分析

为科学地评价比较中美石油安全水平对经济增长的影响程度,文章采用主成分分析方法,选取采储比水平、储量接替率、消费弹性系数、原油价格波动系数、对外依存度和石油占一次能源消费比重等6个要素指标,构成一个新的石油安全指标评价体系,并利用灰色关联方法比较分析了不同时间段内中美两国的石油安全水平与经济增长之间的关联度,得出自21世纪以来,美国经济发展对石油安全水平的依赖程度要远大于中国的结论。     

Unifying CRM and EWOC designs for phase I cancer clinical trials

The main goal of phase I cancer clinical trials is to determine the highest dose of a new therapy associated with an acceptable level of toxicity for the use in a subsequent phase II trial. The continual reassessment method (CRM) [O’Quigley, J., Pepe, M., Fisher, L., 1990. Continual reassessment method: a practical design for phase I clinical trials in cancer. Biometrics 46, 33–48] and escalation with overdose control (EWOC) [Babb, J., Rogatko, A., Zacks, S., 1998. Cancer phase I clinical trials: efficient dose escalation with overdose control. Statist. Med. 17 (10), 1103–1120] are two model-based designs used for phase I cancer clinical trials. A few modifications of the (original) CRM and EWOC have been made by many authors. In this paper, we show how CRM and EWOC can be unified and present a hybrid design. We study the characteristics of the approach of the hybrid design. The comparisons of the three designs (CRM, EWOC, and the hybrid design) are presented by convergence rates and overdose proportions. The simulation results show that the hybrid design generally has faster convergence rates than EWOC and smaller overdose proportions than CRM, especially when the true maximum tolerated dose (MTD) is above the mid-level of the dose range considered. The performance of these three designs is also evaluated in terms of sensitivity to outliers.     

On construction of asymptotically correct confidence intervals

In this paper we discuss constructing confidence intervals based on asymptotic generalized pivotal quantities (AGPQs). An AGPQ associates a distribution with the corresponding parameter, and then an asymptotically correct confidence interval can be derived directly from this distribution like Bayesian or fiducial interval estimates. We provide two general procedures for constructing AGPQs. We also present several examples to show that AGPQs can yield new confidence intervals with better finite-sample behaviors than traditional methods.     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

Bootstrap confidence regions computed from autoregressions of arbitrary order

Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.     

数学中化归问题的教学和实践

本文对数学中化归的方法含义,化归的方法要素和核心作了一些理论探索,提出了化归的三条基本途径：（1）向基本模型化归;（2）向特殊模型化归;（3）向低层模型化归。并对化归方法作了教学实践尝试,从熟悉化、简单化、直观化入手提出了化归是一种重要的解决问题的方法。     

《孟子字义疏证》对《孟子》的阐释和创新

戴震《孟子字义疏证》采用经学训诂的形式对义理内容进行建构,在学术思想史上产生了巨大影响。本文对戴震的义理旨趣、考据特征以及对《孟子》的创新阐释及其缺陷作了分析,认为其过度目的性阐释导致了《疏证》在接受方面的诸多困局。戴震义理学表面上对程朱理学持批判立场,但双方在动机、旨趣和义理内容的建构上不具同源性,戴震把程朱理学瑕疵当成程朱理学本身加以攻击,对原始儒意的理解并没有超越宋儒而进行。戴震对于《孟子》的把握仍有未达,但《疏证》所展现出来的批判精神却影响深远。     

大学物理教学中的课堂提问

大学物理课堂上很少作演示实验,课容量大,内容抽象,根据这一特点,大学物理课堂上的提问就有其自身的特点。课堂提问在整个教学环节中有着极其重要的作用,提问的方式方法不同,产生的效果往往会发生根本的变化。因此,课堂提问应该注意提问的对象、提问的范围、提问的多样性、提问的针对性等等问题。