Diagrams for Set Theory & Probability Problems of Four or More Variables

It is pointed out that in many one-sided testing situations for a real-valued parameter θ, the monotonicity of the power function hinges on the stochastic order of the underlying family of distributions [F_θ] rather than on the stronger property of monotone likelihood ratio of the family. An elementary proof, accessible to students of introductory probability and statistics, is presented.     

Checking the Short‐Term and Long‐Term Hazard Ratio Model for Survival Data

Abstract. The short‐term and long‐term hazard ratio model includes the proportional hazards model and the proportional odds model as submodels, and allows a wider range of hazard ratio patterns compared with some of the more traditional models. We propose two omnibus tests for checking this model, based, respectively, on the martingale residuals and the contrast between the non‐parametric and model‐based estimators of the survival function. These tests are shown to be consistent against any departure from the model. The empirical behaviours of the tests are studied in simulations, and the tests are illustrated with some real data examples.     

非线性协和模型：理论与方法

 本文系统梳理了十多年来非线性协和理论与方法的研究进展,从非线性协和概念的提出开始,对目前已给出的非线性协和的各种不同定义、具有非线性结构的时间序列的非平稳性检验、非线性协和关系的检验、非线性协和模型的参数与非参数估计方法、门限协和模型、以及非线性误差修正模型的研究状况进行了总结。     

统计数据预处理的理论与方法述评

统计数据预处理是提升数据质量的重要阶段,包括数据审查、数据清理、数据转换和数据验证四大步骤。根据处理对象的特点及每一步骤的不同目标,统计数据预处理可采用的方法包括描述及探索性分析、缺失值处理、异常值处理、数据变换技术、信度与效度检验、宏观数据诊断等六大类。选用恰当的方法开展统计数据预处理,有利于保证数据分析结论真实、有效。     

资源租金核算理论与方法研究

 本文在对自然资源价值核算的不同方法予以归纳的基础上,对这些方法得以实施的共同基础—资源租金的核算问题提出了一些不同的观点。认为在联合国等国际组织所发布的《环境经济综合核算体系》（SEEA2003）所推荐的三种资源租金的核算方法中,其中两种“间接”推算法存在理论缺陷,并从理论与实证两个方面进行了论证。     

抽样调查理论与方法的哲学诠释

文章从哲学视角诠释了抽样调查理论和方法的科学性和先进性,并指出抽样调查的理论和方法不但体现了辩证唯物主义的认识论,还体现了唯物辩证法的思想。对于人们正确地认识抽样调查,准确地应用抽样调查,积极地发展抽样调查都是大有裨益的。     

Estimating the Risk of a Down's Syndrome Term Pregnancy Using Age and Serum Markers: Comparison of Various Methods

The risk of an individual woman having a pregnancy associated with Down's syndrome is estimated given her age, α-fetoprotein, human chorionic gonadotropin, and pregnancy-specific β1-glycoprotein levels. The classical estimation method is based on discriminant analysis under the assumption of lognormality of the marker values, but logistic regression is also applied for data classification. In the present work, we compare the performance of the two methods using a dataset containing the data of almost 89,000 unaffected and 333 affected pregnancies. Assuming lognormality of the marker values, we also calculate the theoretical detection and false positive rates for both the methods.     

Theory & Methods: Residual Diagnostic Plots for Checking for Model Mis‐specification in Time Series Regression

This paper considers residuals for time series regression. Despite much literature on visual diagnostics for uncorrelated data, there is little on the autocorrelated case. To examine various aspects of the fitted time series regression model, three residuals are considered. The fitted regression model can be checked using orthogonal residuals; the time series error model can be analysed using marginal residuals; and the white noise error component can be tested using conditional residuals. When used together, these residuals allow identification of outliers, model mis‐specification and mean shifts. Due to the sensitivity of conditional residuals to model mis‐specification, it is suggested that the orthogonal and marginal residuals be examined first.     

经济不确定性的量化测度研究：前沿进展与理论综述

测量经济不确定性是一件重要但又较困难的事情,目前国内外专门研究经济不确定性测量方法的文献并不多。本文梳理了近年来国内外量化测度经济不确定性的文献,从中将零碎的有关经济不确定性的测量方法提炼出来,归纳为三大类：通过寻找合适的经济不确定性替代指标、通过调查数据计算被调查者对当前经济状况和预期的主观感知截面数据偏差（或预测偏差）计算不确定性、通过构建状态空间模型求解作为隐含状态量的经济不确定性。本文详细介绍了每类方法的原理和典型方法,对各类方法做了评述：分析了各类方法的适用场景和优缺点,探讨了应用每类方法的关键点和难点,并介绍了每类方法的代表性应用实例。本文清晰、全面地展示了目前量化测度经济不确定性的前沿进展和理论发展,为研究经济不确定性夯实基础工作,补缺了近年来国内在量化测度经济不确定性方法综述这一领域的空白。     

统计学、信息论、模糊数学与不确定性

一、不确定性的种类与本质统计学信息论或模糊数学中所说的不确定性,都是从英文Uncertainty翻释过来的,由美国Delair公司1981年编辑出版的《新韦氏英语辞典》中注明:“不确定性是不确定的性质或状态。”“不确定的包括:不肯定的、令人疑惑的、含糊的、不确切了解的、未决定的、不明确的、不可靠的、模糊的、不稳定的、无规则的、变化无常的、偶然的等等。”可见,不确定性的表现形式很多,按其产生的根源可分为:     

Theory & Methods: Why do we do it? Statisticians and the Practice of Statistics

There has been no work done on why statisticians have chosen their particular profession. With the increasing emphasis on the development of biotechnology, it seems important to encourage people to take up statistics and to offer the perspective that the study of statistics brings. This paper is an attempt to develop a preliminary understanding, by open-ended in-depth interviewing, of the personal backgrounds that have encouraged present practising statisticians to move into this field, and to see how they experience their work.     

An Analysis of Swendsen–Wang and Related Sampling Methods

Convergence rates, statistical efficiency and sampling costs are studied for the original and extended Swendsen–Wang methods of generating a sample path { S _j , j ≥1} with equilibrium distribution π , with r distinct elements, on a finite state space X of size N ₁. Given S _{j -1}, each method uses auxiliary random variables to identify the subset of X from which S _j is to be randomly sampled. Let π_min and π_max denote respectively the smallest and largest elements in π and let N_r denote the number of elements in π with value π_max. For a single auxiliary variable, uniform sampling from the subset and ( N ₁− N_r )π_min+ N_r π_max≈1, our results show rapid convergence and high statistical efficiency for large π_min/π_max or N_r / N ₁ and slow convergence and poor statistical efficiency for small π_min/π_max and N_r / N₁ . Other examples provide additional insight. For extended Swendsen–Wang methods with non-uniform subset sampling, the analysis identifies the properties of a decomposition of π( x ) that favour fast convergence and high statistical efficiency. In the absence of exploitable special structure, subset sampling can be costly regardless of which of these methods is employed.     

概化理论两侧面设计方差分量及其变异量估计方法比较

文章针对正态分布数据,对比Traditional方法、Bootstrap方法和MCMC方法在两侧面交叉设计(p×i×h)和两侧面嵌套设计(p×(i:h))下各个方差分量的估计精度,为实际应用提供参考。使用R软件模拟1000批数据,并在R软件上实现三种方法的方差分量及其变异量估计。结果表明:(1)相较于Traditional方法和MCMC方法,相同条件下,Bootstrap方法估计的方差分量及其变异量结果更为理想;(2)对于两侧面交叉设计和两侧面嵌套设计,在正态分布数据下,建议优先使用Bootstrap方法。     

Spatio‐temporal Ornstein–Uhlenbeck Processes: Theory,Simulation and Statistical Inference

Spatio‐temporal modelling is an increasingly popular topic in Statistics. Our paper contributes to this line of research by developing the theory, simulation and inference for a spatio‐temporal Ornstein–Uhlenbeck process. We conduct detailed simulation studies and demonstrate the practical relevance of these processes in an empirical study of radiation anomaly data. Finally, we describe how predictions can be carried out in the Gaussian setting.