A Note on Ergodic Processes Prediction via Estimation of the Conditional Mode Function

We establish the uniform almost-sure convergence of a kernel estimate of the conditional density for an ergodic process. A useful application to the prediction of the ergodic process via the conditional mode function is also given.     

On a class of bivariate mixed Sarmanov distributions

Multivariate distributions are more and more used to model the dependence encountered in many fields. However, classical multivariate distributions can be restrictive by their nature, while Sarmanov's multivariate distribution, by joining different marginals in a flexible and tractable dependence structure, often provides a valuable alternative. In this paper, we introduce some bivariate mixed Sarmanov distributions with the purpose to extend the class of bivariate Sarmanov distributions and to obtain new dependency structures. Special attention is paid to the bivariate mixed Sarmanov distribution with Poisson marginals and, in particular, to the resulting bivariate Sarmanov distributions with negative binomial and with Poisson‐inverse Gaussian marginals; these particular types of mixed distributions have possible applications in, for example modelling bivariate count data. The extension to higher dimensions is also discussed. Moreover, concerning the dependency structure, we also present some correlation formulas.     

Selection bias for treatments with positive Phase 2 results

In drug development, treatments are most often selected at Phase 2 for further development when an initial trial of a new treatment produces a result that is considered positive. This selection due to a positive result means, however, that an estimator of the treatment effect, which does not take account of the selection is likely to over‐estimate the true treatment effect (ie, will be biased). This bias can be large and researchers may face a disappointingly lower estimated treatment effect in further trials. In this paper, we review a number of methods that have been proposed to correct for this bias and introduce three new methods. We present results from applying the various methods to two examples and consider extensions of the examples. We assess the methods with respect to bias of estimation of the treatment effect and compare the probabilities that a bias‐corrected treatment effect estimate will exceed a decision threshold. Following previous work, we also compare average power for the situation where a Phase 3 trial is launched given that the bias‐corrected observed Phase 2 treatment effect exceeds a launch threshold. Finally, we discuss our findings and potential application of the bias correction methods.     

Book Reviews

Books reviewed:
Alan A. Grometste, The Roots of Things: Topics in Quantum Mechanics
The British Medical Association, Health and Environmental Impact Assessment: An Integrated Approach
Kate M. Scow, Graham E. Fogg, David E. Hinton, and Michael L. Johnson, Integrated Assessment of Ecosystem Health     

Fitting Second-Order Finite Mixture Models to Data with Many Censored Values Using Maximum Likelihood Estimation

Finite mixture models, that is, weighted averages of parametric distributions, provide a powerful way to extend parametric families of distributions to fit data sets not adequately fit by a single parametric distribution. First-order finite mixture models have been widely used in the physical, chemical, biological, and social sciences for over 100 years. Using maximum likelihood estimation, we demonstrate how a first-order finite mixture model can represent the large variability in data collected by the U.S. Environmental Protection Agency for the concentration of Radon 222 in drinking water supplied from ground water, even when 28% of the data fall at or below the minimum reporting level. Extending the use of maximum likelihood, we also illustrate how a second-order finite mixture model can separate and represent both the variability and the uncertainty in the data set.     

Combining forward and backward mortality estimation

Demographers often form estimates by combining information from two data sources—a challenging problem when one or both data sources are incomplete. A classic example entails the construction of death probabilities, which requires death counts for the subpopulations under study and corresponding base population estimates. Approaches typically entail ‘back projection', as in Wrigley and Schofield's seminal analysis of historical English data, or ‘inverse’ or ‘forward projection’ as used by Lee in his important reanalysis of that work, both published in the 1980s. Our paper shows how forward and backward approaches can be optimally combined, using a generalized method of moments (GMM) framework. We apply the method to the estimation of death probabilities for relatively small subpopulations within the United States (men born 1930–39 by state of birth by birth cohort by race), combining data from vital statistics records and census samples.     

Conditional Monte Carlo Gradient Estimation in Economic Design of Control Limits

The economic approach to determining the optimal control limits of control charts requires estimating the gradient of the expected cost function. Simulation is a very general methodology for estimating the expected costs, but for estimating the gradient, straightforward finite difference estimators can be inefficient. We demonstrate an alternative approach based on smoothed perturbation analysis (SPA), also known as conditional Monte Carlo. Numerical results and consequent design insights are obtained in determining the optimal control limits for exponentially weighted moving average and Bayes charts. The results indicate that the SPA gradient estimators can be significantly more efficient than finite difference estimators, and that a simulation approach using these estimators provides a viable alternative to other numerical solution techniques for the economic design problem.     

中国农业全要素生产率增长分布的动态演进机制”

在使用经典DEA-Malmquist生产率指数分析方法对中国各省份1979—2010年间农业全要素生产率(TFP)进行核算的基础上,采用Kernel核密度估计方法刻画农业TFP增长分布的形状动态,应用马尔科夫链法考察农业TFP增长的分布动态,从增长的分布形状和内部流动性两个角度来评估中国农业TFP增长省区分布的动态演进机制。研究表明:一方面,1980—2010年间中国农业相对全要素生产率经历了明显的从"单峰"分布到"双峰"分布再到"单峰"分布的变化过程。绝大多数省份农业TFP存在明显的增长趋势,尤其是技术进步增速显著,技术效率则普遍存在恶化现象;另一方面,省际间农业TFP增长差异明显,可将其分为低水平、中低水平、中高水平和高水平四个"俱乐部","两极"分化现象明显,表现为明显的"中间小、两头大"分布格局,绝对趋同现象很难实现。     

关于多维指标抽样调查中删除指标的均值估计

针对多维度指标抽样调查情况,运用多变量幂函数逼近理论,对多指标中删除的指标构造出一类依赖于保留指标的估计量,通过对其性质的讨论,得出了该估计量的抽样误差与样本量的倒数同阶的结论。在抽样调查的实际应用中,可以根据给定的抽样误差,对部分指标进行调查,未被调查指标的均值通过调查指标值的估计去实现,从而达到了解全部指标信息的目的。     

Polya后验方法在有限总体抽样估计中的模拟研究

polya后验方法作为一种无信息贝叶斯估计方法,在有限总体抽样中,通过观测的样本,构造一系列的模拟总体,然后进行统计推断。通过统计模拟研究了polya后验方法估计的一些特点,并和Bootstrap方法进行比较。模拟结果显示:polya后验方法能够很好地估计总体的均值,随着样本量的增大,估计值与真值的差距越来越小。采用polya后验方法构造的置信区间区间长度较小,能够很好地覆盖真值。