Statistical Inference Enables Bad Science; Statistical Thinking Enables Good Science

ABSTRACT

Scientific research of all kinds should be guided by statistical thinking: in the design and conduct of the study, in the disciplined exploration and enlightened display of the data, and to avoid statistical pitfalls in the interpretation of the results. However, formal, probability-based statistical inference should play no role in most scientific research, which is inherently exploratory, requiring flexible methods of analysis that inherently risk overfitting. The nature of exploratory work is that data are used to help guide model choice, and under these circumstances, uncertainty cannot be precisely quantified, because of the inevitable model selection bias that results. To be valid, statistical inference should be restricted to situations where the study design and analysis plan are specified prior to data collection. Exploratory data analysis provides the flexibility needed for most other situations, including statistical methods that are regularized, robust, or nonparametric. Of course, no individual statistical analysis should be considered sufficient to establish scientific validity: research requires many sets of data along many lines of evidence, with a watchfulness for systematic error. Replicating and predicting findings in new data and new settings is a stronger way of validating claims than blessing results from an isolated study with statistical inferences.     

金融周期、金融波动与中国经济增长——基于省际面板门槛模型的研究

本文应用面板门槛模型，研究了2005-2017年间我国31个省（市、自治区）金融波动对经济增长的影响。研究发现，随着金融周期所处阶段的变化，金融波动对经济增长会产生显著的非对称性双重门槛效应，主要体现为如下两点：首先，金融周期处于膨胀期、平稳期和萧条期时金融波动对经济增长会产生负向影响，但从影响系数值的大小来看，处于膨胀期时最大，是后两者的2倍之多，处于平稳期时最小且并不显著；其次，分区域的稳健性检验表明，金融发展水平高的区域双重门槛值出现得早，且两个门槛值间的区间要比金融发展水平低的区域宽28%。这些结论说明，经济增长对于金融波动的容忍弹性会随着金融周期所处的阶段而变化，金融发展水平的提高会放大经济增长对金融波动的容忍区间，但也会加速金融周期处于膨胀期时爆发金融危机的可能性，这使得当前我国存在着进一步发展金融水平和严控金融风险的矛盾，对此本文也提出了相应的政策建议。     

网络社区发现算法在流动表建模中的设计与应用

代际流动表可以统计子代与其父代社会地位配对数据的交互频数，反映了社会资源占有的优劣势在父子两代人之间的比较。对财富、阶级、特权等社会基本特征演变的实证考察，均依赖于代际流动表的量化分析。对数线性模型是流动表建模分析的基本工具，通过对列联表单元格频数进行拟合，可以识别流动表行分类与列分类之间的强弱交互效应，刻画父子社会地位间的交互结构。本文利用复杂网络社区发现算法分析父子社会地位的关联结构，针对简约对数线性模型拟合精度不够的问题，提出一种新的建模思路：利用社区发现算法对简约对数线性模型的残差列联表进行关联关系挖掘，将发现的社区效应作为附加参数约束引入原对数线性模型，以改善数据的拟合情况。由于该方法只在原简约对数线性模型中增加了一个参数约束，因此仍可以保证建模结果的简洁性及理论意义，同时社区效应补充了原对数线性模型对经验数据结构的解读。论文用此方法对来源于中国综合社会调查数据的经验代际职业流动表进行建模分析，较好地解释了子代职业阶层与父代职业阶层间的关联模式。     

基于超总体模型的设计效应分解

本文基于超总体模型研究抽样调查中设计效应的计算问题。首先以随机效应模型为基础，明确了简单随机、二阶段、不等概率和分层抽样对应的超总体模型，进而通过所给模型推导出分层、类集、加权单因素设计效应的计算公式和多因素组合的设计效应计算公式并给出了对应估计量，公式表明：多因素同时存在的组合设计效应等于对应单因素设计效应的乘积。最后，对设计效应的理论值、估计值和真实值之间的关系进行了蒙特卡洛仿真，并利用相对偏倚、相对均方误进行了评价。本文的研究，对复杂抽样设计中正确计算、使用设计效应具有指导意义。     

基于心智模型的恐怖主义袭击扩展式演化博弈分析

政府反恐措施与恐怖分子袭击手段存在着相互观察、适应性演化的过程。本文首先构建了政府作为先行动者、恐怖分子作为后行动者的斯塔克伯格博弈模型，进一步建立了恐怖袭击问题的扩展式演化博弈模型。由于扩展式演化博弈的均衡分析需要考虑代际内和代际间不同层次的信念学习，造成了演化分析的复杂性。本文将"心智模型"概念引入到演化博弈，采取了心智模型演化解的分析方法，得出了简化后的演化均衡解。最后，结合新疆墨玉县6.28暴恐事件进行算例分析，比较怀特流形演化解和心智模型演化解的差异。心智模型演化解的结果表明，根据恐怖分子群体中选择袭击比例是否高于临界值，政府策略收敛到防御或者不防御。该求解方法通过将普遍接受的社会规范引入到演化过程分析，不仅简化了怀特流形的分析过程，而且均衡解展示了更为丰富的、更为切合实际管理问题的演化特征。     

Comparing Possibly Misspecified Forecasts

Abstract

Recent work has emphasized the importance of evaluating estimates of a statistical functional (such as a conditional mean, quantile, or distribution) using a loss function that is consistent for the functional of interest, of which there is an infinite number. If forecasters all use correctly specified models free from estimation error, and if the information sets of competing forecasters are nested, then the ranking induced by a single consistent loss function is sufficient for the ranking by any consistent loss function. This article shows, via analytical results and realistic simulation-based analyses, that the presence of misspecified models, parameter estimation error, or nonnested information sets, leads generally to sensitivity to the choice of (consistent) loss function. Thus, rather than merely specifying the target functional, which narrows the set of relevant loss functions only to the class of loss functions consistent for that functional, forecast consumers or survey designers should specify the single specific loss function that will be used to evaluate forecasts. An application to survey forecasts of U.S. inflation illustrates the results.     

Spectral goodness of fit for network models

We introduce a new statistic, ‘spectral goodness of fit’ (SGOF) to measure how well a network model explains the structure of the pattern of ties in an observed network. SGOF provides a measure of fit analogous to the standard R² in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied.     

Semiparametric multiple kernel estimators and model diagnostics for count regression functions

Abstract

This study concerns semiparametric approaches to estimate discrete multivariate count regression functions. The semiparametric approaches investigated consist of combining discrete multivariate nonparametric kernel and parametric estimations such that (i) a prior knowledge of the conditional distribution of model response may be incorporated and (ii) the bias of the traditional nonparametric kernel regression estimator of Nadaraya-Watson may be reduced. We are precisely interested in combination of the two estimations approaches with some asymptotic properties of the resulting estimators. Asymptotic normality results were showed for nonparametric correction terms of parametric start function of the estimators. The performance of discrete semiparametric multivariate kernel estimators studied is illustrated using simulations and real count data. In addition, diagnostic checks are performed to test the adequacy of the parametric start model to the true discrete regression model. Finally, using discrete semiparametric multivariate kernel estimators provides a bias reduction when the parametric multivariate regression model used as start regression function belongs to a neighborhood of the true regression model.     

On the consistency and the robustness in model selection criteria

Abstract

In the model selection problem, the consistency of the selection criterion has been often discussed. This paper derives a family of criteria based on a robust statistical divergence family by using a generalized Bayesian procedure. The proposed family can achieve both consistency and robustness at the same time since it has good performance with respect to contamination by outliers under appropriate circumstances. We show the selection accuracy of the proposed criterion family compared with the conventional methods through numerical experiments.     

空气污染治理与公众健康———来自“大气十条”政策的证据

为探究《大气污染防治行动计划》 (以下简称“大气十条”)的健康效应,本文基于中国健康与营养调查(CHNS)数据及省级面板数据,利用基于多项Logit模型的双重差分法(Logit-DID),从微观与宏观两个维度考察“大气十条”政策的健康改善效应及其传导机制,并进一步通过异质性分析探讨环境健康不平等的内在原因 研究发现:“大气十条”实施带来显著的健康效应,该政策不仅能有效控制与空气污染高度相关疾病的发病率和死亡占比,还能够间接降低受空气污染影响较小的疾病病情。其作用机理主要通过控制PM2.5浓度改善公众健康,同时该政策对二氧化硫(SO2)、氮氧化物、烟(粉)尘等其 他污染物浓度的下降起到了协同作用。进一步分析显示环境福利不公平的现象依然存在,“大气十条”政 策显著降低了疾病高发人群的发病率,且对女性、城镇居民和低、高年龄段等疾病高发人群的健康影响更显著。本文为政府构建环境健康公平发展路径,推进“健康中国”战略提供了经验证据和政策借鉴。