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多参数非参数融合学习：结合数据深度与置信分布AI 解读

Fusion learning refers to synthesizing inferences from multiple sources or studies to make a more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on parametric model assumptions, such as normality, which often do not hold in practice. We propose a general nonparametric fusion learning framework for synthesizing inferences for multiparameters from different studies. The main tool…

借助置信分布拓展Fisher随机化检验：推断、组合与融合学习AI 解读

Abstract The flexibility and wide applicability of the Fisher randomization test (FRT) make it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions. Such a connection leads to development’s of (i) an unambiguous procedure for inversion of FRTs to generate…

iFusion：个体化融合学习AI 解读

Inferences from different data sources can often be fused together, a process referred to as “fusion learning,” to yield more powerful findings than those from individual data sources alone. Effective fusion learning approaches are in growing demand as increasing number of data sources have become easily available in this big data era. This article proposes a new fusion learning approach, called “iFusion,” for drawing efficient individualized inference by fusing learnings…

Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the half-space depth is shown to have many desirable properties and broad applicability. However, the empirical half-space depth is zero outside the convex hull of the data. This property has rendered the empirical…

仅用汇总统计量的异质研究多变量元分析：效率与稳健性AI 解读

Meta-analysis has been widely used to synthesize evidence from multiple studies for common hypotheses or parameters of interest. However, it has not yet been fully developed for incorporating heterogeneous studies, which arise often in applications due to different study designs, populations, or outcomes. For heterogeneous studies, the parameter of interest may not be estimable for certain studies, and in such a case, these studies are typically excluded from conventional…

离散数据的精确荟萃分析及其稀有事件列联表应用AI 解读

) associated with the exact tests from individual studies. It encompasses a broad class of exact meta-analysis methods, as it permits broad choices for the combining elements, such as tests used in individual studies, and any parameter of interest. The approach yields statements that explicitly account for the impact of individual studies on the overall inference, in terms of efficiency/power and the type I error rate. Those statements also give rises to empirical methods…

DD 分类器：基于深度对深度图的非参数分类方法AI 解读

Using the DD-plot (depth vs. depth plot), we introduce a new nonparametric classification algorithm and call it DD-classifier. The algorithm is completely nonparametric, and it requires no prior knowledge of the underlying distributions or the form of the separating curve. Thus, it can be applied to a wide range of classification problems. The algorithm is completely data driven and its classification outcome can be easily visualized in a two-dimensional plot regardless of…

多重风险同步监测中极端事件的阈值划分AI 解读

This article develops a threshold system for monitoring airline performance. This threshold system divides the sample space into regions with increasing levels of risk and allows instant assessments of risk level of any observed airline performance. Of particular concern is the performance with extreme risk. In this article, a multivariate extreme value theory approach is used to establish thresholds for signaling varying levels of extremeness in the context of simultaneous…

基于数据深度的多变量间距：非参数多变量容忍区域的构造AI 解读

This paper introduces and studies multivariate spacings. The spacings are developed using the order statistics derived from data depth. Specifically, the spacing between two consecutive order statistics is the region which bridges the two order statistics, in the sense that the region contains all the points whose depth values fall between the depth values of the two consecutive order statistics. These multivariate spacings can be viewed as a data-driven realization of the…

基于数据深度的多元分析：描述统计、图形与推断（含讨论及作者答复）AI 解读

A data depth can be used to measure the “depth” or “outlyingness” of a given multivariate sample with respect to its underlying distribution. This leads to a natural center-outward ordering of the sample points. Based on this ordering, quantitative and graphical methods are introduced for analyzing multivariate distributional characteristics such as location, scale, bias, skewness and kurtosis, as well as for comparing inference methods. All graphs are one-dimensional curves…

基于数据深度与自助法的极限 P 值概念AI 解读

In this article we propose some new notions of limiting P values for hypothesis testing. The limiting P value (LP) here not only provides the usual attractive interpretation of a P value as the strength in support of the null hypothesis coming from the observed data, but also has several advantages. First, it allows us to resample directly from the empirical distribution (in the bootstrap implementations), rather than from the estimated population distribution satisfying the…

基于自助法的相依与独立观测控制图AI 解读

Shewhart charts are widely accepted as standard tools for monitoring manufacturing processes of univariate, independent “nearly” normal measurements. They are not as well developed beyond these types of data. We generalize the idea of Shewhart charts to cover other types of data commonly encountered in practice. More specifically, we develop some valid control charts for dependent data and for independent data that are not necessarily “nearly” normal. We derive the proposed…

基于数据深度的质量指数与多元秩检验AI 解读

Let F and G be the distribution functions of two given populations on Rp, p ≥ 1. We introduce and study a Parameter Q = Q(F, G), which measures the Overall “outlyingness” of population G relative to population F. The Parameter Q can be defined using any concept of data depth. Its value ranges from 0 to 1, and is .5 when F and G are identical. We show that within the dass of elliptical distributions when G departs from F in location or G has a larger spread, or both, the…

方向数据的排序：圆与球面上的数据深度AI 解读

Three notions of depth for directional data, angular simplicial depth (ASD), angular Tukey's depth (ATD) and arc distance depth (ADD), are developed and studied. The empirical versions of these depths give rise to center-outward rankings of angular data which may be regarded as extensions of the usual center-outward ranking on the line. Three medians derived from these depths are examined and compared. Applications in nonparametric classification and in implementing the…

重抽样方法的效率与稳健性AI 解读

It is known that the standard delete-1 jackknife and the classical bootstrap are in general equally efficient for estimating the mean-square-error of a statistic in the i.i.d. setting. However, this equivalence no longer holds in the linear regression model. It turns out that the bootstrap is more efficient when error variables are homogeneous and the jackknife is more robust when they are heterogeneous. In fact, we can divide all the commonly used resampling procedures for…

若干非独立同分布模型下的自助法程序AI 解读

It is shown in this article that the classical i.i.d. bootstrap remains a valid procedure for estimating the sampling distributions of certain symmetric estimators of location, as long as the random observations are independently drawn from distributions with (essentially) a common location. This may be viewed as a robust property of the classical i.i.d. bootstrap. Also included is a study of the second order properties of a different bootstrap procedure proposed by Wu in…

Bootstrap 的部分修正现象AI 解读

The phenomenon of partial $n^{-1/2}$-term correction by the bootstrap in the estimation of sampling distributions of nonstandardized statistics is explained and studied in this note.