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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…

无效工具变量下的因果推断：选择后问题及搜索与抽样方案AI 解读

Abstract Instrumental variable methods are among the most commonly used causal inference approaches to deal with unmeasured confounders in observational studies. The presence of invalid instruments is the primary concern for practical applications, and a fast-growing area of research is inference for the causal effect with possibly invalid instruments. This paper illustrates that the existing confidence intervals may undercover when the valid and invalid instruments are hard…

计算高效且数据自适应的高维变点推断AI 解读

Abstract High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two statistics based on aggregating cumulative sum statistics over all dimensions and possible changepoints by taking their maximum and summation, respectively, are asymptotically independent under some mild conditions. Hence, we are able to…

最小截尾平方估计量成为最大似然估计量的一种模型AI 解读

Abstract The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of h ‘good’ observations among n observations and applies least squares on that subsample. We formulate a model in which this estimator is maximum likelihood. The model has ‘outliers’ of a new type, where the outlying observations are drawn from a distribution with values outside the realized range of h ‘good’, normal observations. The LTS estimator is found to…

自回归最优传输模型AI 解读

Abstract Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps…

不识别联合分布时非可忽略无应答数据的均值泛函推断AI 解读

Abstract We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to non-ignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for n-estimability of the mean functional. This condition naturally strengthens the identifying…

比较潜变量模型的核Stein检验AI 解读

Abstract We propose a kernel-based nonparametric test of relative goodness of fit, where the goal is to compare two models, both of which may have unobserved latent variables, such that the marginal distribution of the observed variables is intractable. The proposed test generalizes the recently proposed kernel Stein discrepancy (KSD) tests (Liu et al., Proceedings of the 33rd international conference on machine learning (pp. 276–284); Chwialkowski et al., (2016), In…

变分矩方法AI 解读

Abstract The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. We introduce a very general class of estimators called the variational method of moments (VMM), motivated by a variational minimax reformulation of optimally weighted generalized method of moments for finite sets of moments. VMM controls infinitely for many moments characterized by…

稀疏 Kronecker 积分解：图像回归信号区域检测的一般框架AI 解读

Abstract This paper aims to present the first Frequentist framework on signal region detection in high-resolution and high-order image regression problems. Image data and scalar-on-image regression are intensively studied in recent years. However, most existing studies on such topics focussed on outcome prediction, while the research on region detection is rather limited, even though the latter is often more important. In this paper, we develop a general framework named…

流形提升：将 MCMC 扩展到观测噪声趋零的情形AI 解读

Abstract Standard Markov chain Monte Carlo methods struggle to explore distributions that concentrate in the neighbourhood of low-dimensional submanifolds. This pathology naturally occurs in Bayesian inference settings when there is a high signal-to-noise ratio in the observational data but the model is inherently over-parametrised or nonidentifiable. In this paper, we propose a strategy that transforms the original sampling problem into the task of exploring a distribution…

分布偏移下的统计检验AI 解读

Abstract We introduce statistical testing under distributional shifts. We are interested in the hypothesis P*∈H0 for a target distribution P*, but observe data from a different distribution Q*. We assume that P* is related to Q* through a known shift τ and formally introduce hypothesis testing in this setting. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set (similarly to sampling importance resampling) and…

函数参数的快速、公平同时置信带AI 解读

Abstract Quantifying uncertainty using confidence regions is a central goal of statistical inference. Despite this, methodologies for confidence bands in functional data analysis are still underdeveloped compared to estimation and hypothesis testing. In this work, we present a new methodology for constructing simultaneous confidence bands for functional parameter estimates. Our bands possess a number of positive qualities: (1) they are not based on resampling and thus are…

随机试验与真实世界数据的弹性整合：处理效应异质性估计AI 解读

Abstract We propose a test-based elastic integrative analysis of the randomised trial and real-world data to estimate treatment effect heterogeneity with a vector of known effect modifiers. When the real-world data are not subject to bias, our approach combines the trial and real-world data for efficient estimation. Utilising the trial design, we construct a test to decide whether or not to use real-world data. We characterise the asymptotic distribution of the test-based…

跳跃扩散过程的精确蒙特卡洛似然推断AI 解读

Abstract Statistical inference for discretely observed jump-diffusion processes is a complex problem which motivates new methodological challenges. Thus, existing approaches invariably resort to time-discretisations which inevitably lead to approximations in inference. In this paper, we give the first general collection of methodologies for exact (in this context meaning discretisation-free) likelihood-based inference for discretely observed finite activity jump-diffusions.…

同质性检验：稀疏函数型数据的困难AI 解读

Abstract Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both…

基于置换与求和检验的真实发现比例保证AI 解读

Abstract Sum-based global tests are highly popular in multiple hypothesis testing. In this paper, we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDPs), simultaneously over all subsets of hypotheses. These simultaneous inferences come for free, i.e., without any adjustment of the α-level, whenever a global test is used. Our method allows for an exploratory approach, as simultaneity…

复杂纵向研究中的近端因果推断AI 解读

Abstract A standard assumption for causal inference about the joint effects of time-varying treatment is that one has measured sufficient covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values, also known as ‘sequential randomization assumption (SRA)’. SRA is often criticized as it requires one to accurately measure all confounders. Realistically, measured covariates can rarely capture all confounders with certainty.…

用于最优动态治疗策略估计的贝叶斯似然回归AI 解读

Abstract Clinicians often make sequences of treatment decisions that can be framed as dynamic treatment regimes. In this paper, we propose a Bayesian likelihood-based dynamic treatment regime model that incorporates regression specifications to yield interpretable relationships between covariates and stage-wise outcomes. We define a set of probabilistically-coherent properties for dynamic treatment regime processes and present the theoretical advantages that are…

高维面板函数型时间序列的统计推断AI 解读

Abstract In this paper, we develop statistical inference tools for high-dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis decomposition of functional data in these spaces, and derive Gaussian and multiplier bootstrap approximations for sums of high-dimensional functional time series. These results have numerous important statistical consequences.…

存在测量误差的连续处理效应非参数估计AI 解读

Abstract We identify the average dose–response function (ADRF) for a continuously valued error-contaminated treatment by a weighted conditional expectation. We then estimate the weights nonparametrically by maximising a local generalised empirical likelihood subject to an expanding set of conditional moment equations incorporated into the deconvolution kernels. Thereafter, we construct a deconvolution kernel estimator of ADRF. We derive the asymptotic bias and variance of…