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多协变量预期短缺回归的稳健估计与推断AI 解读

Abstract Expected shortfall (ES), also known as superquantile or conditional value-at-risk, is an important measure in risk analysis and stochastic optimisation and has applications beyond these fields. In finance, it refers to the conditional expected return of an asset given that the return is below some quantile of its distribution. In this paper, we consider a joint regression framework recently proposed to model the quantile and ES of a response variable simultaneously,…

通过双臂老虎机过程构造策略性两样本检验AI 解读

Abstract This study aims to improve the power of two-sample tests by analysing whether the difference between two population parameters is larger than a prespecified positive equivalence margin. The classic test statistic treats the original data as exchangeable, while the proposed test statistic breaks the structure and proposes employing a two-armed bandit process to strategically integrate the data and thus a strategy-specific test statistic is constructed by combining…

Ying Zhou与Xinyi Zhang对Varimax因子分析论文的讨论AI 解读

We congratulate Rohe and Zeng for their inspiring work on providing theoretical support for Varimax rotation in factor analysis. A key contribution of the article is the demonstration that if the factors in the semi-parametric factor model follow heavy-tailed distribution, then performing principal components analysis (PCA) on the observed data matrix along with Varimax rotation applied to the principal components does produce interpretable explanatory variables. We have the…

Van Werde对《Varimax经典因子分析可进行统计推断》的讨论AI 解读

I would like to point out that the author’s results have potential applications in the theory of random graphs beyond those for block models which are explicitly remarked upon in the paper. In particular, the results could be used to resolve the nonidentifiability associated with random dot product graphs (Athreya et al., 2017, Remark 1). The authors are most likely already aware of this connection: they have previously worked on generalized random dot product graphs in Rohe…

We congratulate Rohe and Zeng on their interesting paper and would like to share two comments and propose one question for their consideration. First, it is impressive to see the large variety of models addressed by the ‘vintage sparse PCA’ (vsp) framework, ranging from traditional factor models to explainable and sparse PCA but also including topic models and stochastic block models. In our view, the demonstration of the broad applicability of the ‘compress and rotate’…

Pargent、Goretzko 与 von Oertzen 对《经典因子分析结合 Varimax 可进行统计推断》的讨论AI 解读

As psychologists, we appreciate Rohe & Zeng’s (R&Z; Rohe & Zeng, 2022) new insights into ‘vintage’ principal component analysis with varimax rotation (PCA+VR). Theories of intelligence and personality, perhaps psychology’s contributions best known outside of our field, have been a direct product of PCA. PCA+VR is still widely used for developing and evaluating psychological tests and questionnaires, although the literature has fought against it in favour of more complex…

Bickel 等对《Varimax 经典因子分析实现统计推断》的讨论意见AI 解读

We compliment the authors for their unification of old and new latent variable models. Their motivation seems to have come from Thurstone’s Factor Analysis and the wish to explain the somewhat mysterious success of Kaiser’s Varimax rule in that context. However, their major applications and notation stem from overlapping network community detection and Latent Dirichlet Allocation (LDA) (Blei et al., 2003). Inference for these models can be unified in another way via a…

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VanderWeele对《Varimax传统因子分析可进行统计推断》的讨论AI 解读

Rohe and Zeng (2022) have provided important results concerning properties of ‘vintage factor analysis’ that assist with interpretability, especially for non-Gaussian and leptokurtic data. I would like to focus my remarks on one particular comment, also present in Thurstone (1935) that, one aims “to ensure that each factor…. corresponds to a ‘scientifically meaningful category.’” This is an important goal, but I would argue that (i) questions of the meaning of factors always…

Tao Wang 对《Varimax 旋转的经典因子分析可进行统计推断》的讨论AI 解读

I congratulate the authors on their excellent paper studying the fundamental mechanism of PCA with the Varimax rotation. The paper thoughtfully establishes theorems to demonstrate that the Varimax rotation can supply an unified estimating technique for a wide range of semiparametric factor models. My discussion will be primarily centred on clarification and potential extensions. The paper illustrates that if PCA is performed on a matrix with independent elements, PCA with…

Yang Liu对《采用Varimax旋转的传统因子分析可实现统计推断》的讨论AI 解读

I congratulate Rohe and Zeng for the fascinating piece of work. They discovered that sparse principle components analysis (PCA) with Varimax rotation (vsp) identifies and consistently recovers latent factors in a broad class of semi-parametric factor models. I have a number of comments to share regarding identification assumptions, asymptotic results, and interpretation of factors. Identification Assumptions. The identification of the low-rank matrix M=ZBY⊤ (when treated as…

Kaizheng Wang 对《采用 Varimax 的传统因子分析可实现统计推断》的讨论AI 解读

I congratulate Drs. Rohe and Zeng for their elegant paper that advances our understanding of the classical Varimax algorithm. Varimax was originally proposed by Kaiser (1958) as an analytic criterion for determining interpretable factors. Despite its extensive applications and tremendous success, theoretical understanding is still lacking. Statisticians are further perplexed by negative results showing the nonidentifiability of Gaussian factor models. Toward resolving the…

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倪晓月对《Varimax 旋转的传统因子分析可进行统计推断》的讨论AI 解读

I want to congratulate Rohe and Zeng on solving a long-time puzzle (and fight between statisticians and practitioners) of ‘why/whether the varimax rotation works’. Their inspiring results have some implications in the literature of latent space models for social networks (Hoff, 2021; Hoff et al., 2002). One of the appealing features of the latent space model is that one can extract the latent factors and analyse the unobserved features through the latent positions. However,…

Anru Zhang; Rungang Han and Anru R Zhang’s contribution to the Discussion of “Vintage Factor Analysis with Varimax Performs Statistical Inference” by Rohe &

Mark Pilling 对《采用 Varimax 的传统因子分析可进行统计推断》的讨论AI 解读

Thanks to the authors for their very interesting, thoughtful, and thorough reconsideration of the topic of factor analysis. We know to be a weakness of factor analysis that an issue is that analysts must chose the type of rotation (e.g., SPSS lists Varimax, Direct Oblimin, Quartimax, Equamax, & Promax) to use, and this choice tends to be subjectively based on how useful or interpretable the rotation was in the context of the study. So multiple rotations might be considered.…

Joshua Cape 对《采用 Varimax 的经典因子分析实现统计推断》的讨论AI 解读

I congratulate Professor Rohe and Dr Zeng on their illuminating paper. Their broad contributions will no doubt redouble contemporary research activity in multivariate analysis for years to come. Even the paper’s appendices are full of valuable gems, not to be overlooked by readers. Rohe and Zeng contextualize their findings vis-à-vis classical developments in psychometrics and statistics. This choice is apt, for the authors champion a newfound understanding of varimax factor…

Christine P Chai 对《Varimax 旋转的经典因子分析可进行统计推断》的讨论AI 解读

Disclaimer: The opinions and views expressed here are those of the author and do not necessarily state or reflect those of Microsoft. Rohe and Zeng (2020) made an advancement to show that Vintage Factor Analysis with Varimax can perform statistical inference, with a wide range of applications. I appreciate that the authors made the whole vsp (Vintage Sparse PCA) package1 available in R for the general public. I have several questions regarding the paper: Why was Multiple…

何银秋、顾玉琪、应志良对《使用 Varimax 的经典因子分析可进行统计推断》的讨论AI 解读

We congratulate the authors on an impressive paper that demystifies the popular Varimax rotation. They showed that the Varimax rotation can identify true axes of latent factors under the leptokurtic condition in a low-rank semiparametric factor model Different from (1), the exploratory Item Factor Analysis (IFA), widely used in social and behavioural sciences, adopts a nonlinear transformation of the low-rank structure: where the binary data matrix R contains N individuals’…

对《结合 Varimax 的经典因子分析可实现统计推断》的致谢提议与讨论AI 解读

I congratulate the authors on their article, which brings together theory and methods from the established areas of factor analysis and independent components analysis, combines these with new results, and applies the combination to the developing research area of matrix-variate data analysis. To many statisticians, factor analysis is simply a model that specifies that the covariance matrix Σ of a d-variate population is equal to a rank-k matrix M=HH⊤ (with k

陈云霄与徐恭军对《采用Varimax的经典因子分析可进行统计推断》的讨论AI 解读

We congratulate Rohe and Zeng for this insightful paper that elegantly connects psychometric methods and statistical and machine learning applications. We would like to mention several lines of related research. First, the problem is closely related to the latent variable selection problems (e.g., Y. Chen et al., 2015; Xu & Shang, 2018), where regularised estimation procedures are proposed to learn sparse loading structures. In fact, the vsp procedure can be viewed as the…

Kuldeep Kumar 对《传统 Varimax 因子分析实现统计推断》的讨论AI 解读

Data Analysts are quite often confused between principal component analysis (PCA) and factor analysis. Both are the same data reduction techniques that are immensely helpful in big data analysis in many other areas. I personally think factor analysis is just an offshoot of PCA and as the authors have mentioned PCA with Varimax is a vintage data analysis technique. So, should the title of the paper be Vintage PCA with Varimax performing statistical inference? I am quite…

面板数据非线性双重差分的简便方法AI 解读

Summary I derive simple, flexible strategies for difference-in-differences settings where the nature of the response variable may warrant a nonlinear model. I allow for general staggered interventions, with and without covariates. Under an index version of parallel trends, I show that average treatment effects on the treated (ATTs) are identified for each cohort and calendar time period in which a cohort was subjected to the intervention. The pooled quasi-maximum likelihood…

工具变量分位数回归的一阶段表示AI 解读

Summary This paper develops a first-stage linear regression representation for an instrumental variables (IV) quantile regression (QR) model. The quantile first stage is analogous to the least-squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural…