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处理决策存在策略互动的处理效应模型AI 解读

This study considers treatment effect models in which others’ treatment decisions can affect both one’s own treatment and outcome. Focusing on the case of two-player interactions, we formulate treatment decision behavior as a complete information game with multiple equilibria. Using a latent index framework and assuming a stochastic equilibrium selection, we prove that the marginal treatment effect from one’s own treatment and that from the partner are identifiable on the…

简单合约的结构分析AI 解读

This paper provides an econometric framework for analyzing two-period simple contracts where an agent chooses between a fixed-price option and a cost-reimbursement option provided by a principal in each contracting period. First, we propose a consistent procedure for testing the null hypothesis of a corresponding cost function being linear, which is widely assumed for tractability in the literature. Motivated by the rejection of such a null based on our empirical data, next…

Olley–Pakes 生产函数估计量的识别与影响函数AI 解读

In this paper, we reconsider the assumptions that ensure the identification of the production function in Olley and Pakes (1996, Econometrica 64, 1263–1297). We show that an index restriction plays a crucial role in the identification, especially if the capital stock is measured by the perpetual inventory method. The index restriction is not sufficient for identification under sample selectivity. The index restriction makes it possible to derive the influence function and…

局部平坦函数系数回归的极限理论AI 解读

Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. The paper develops new asymptotics that take account of shape characteristics…

空间数据的非参数预测AI 解读

We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptotic properties. Finite sample performance is assessed in a Monte Carlo study that also compares our algorithm to a rival nonparametric method based on the infinite $AR$ representation of the dynamics of the data. Finally, we apply our methodology to predict…

经典因子分析中的 Varimax 旋转具有统计推断作用AI 解读

Abstract In the 1930s, Psychologists began developing Multiple-Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors. In this form of factor analysis, the Varimax factor rotation redraws the axes through the multi-dimensional factors to make them sparse and thus make them more interpretable. Charles Spearman and many others objected to factor rotations because the factors seem to be…

利用深度条件生成学习检验时间序列的马尔可夫性AI 解读

Abstract The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a nonparametric test for the Markov property in high-dimensional time series via deep conditional generative learning. We also apply the test sequentially to determine the order of the Markov model. We show that the test controls the type-I…

归一化潜在测度因子模型AI 解读

Abstract We propose a methodology for modelling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalised random measures, we consider a prior distribution for a collection of discrete random measures where each measure is a linear combination of a set of latent measures, interpretable as characteristic traits shared by different distributions, with positive random weights. The model is nonidentified and a method for…

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…

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…

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’…

变系数非参数变换模型的模型选择AI 解读

Summary Based on the smoothed partial rank (SPR) loss function, we propose a group LASSO penalized SPR estimator for the varying coefficient nonparametric transformation models, and derive its estimation and model selection consistencies. It not only selects important variables, but is also able to select between varying and constant coefficients. To deal with the computational challenges in the rank loss function, we develop a group forward and backward stagewise algorithm…

潜变量资产定价模型的半参数估计AI 解读

This paper studies semiparametric identification and estimation of consumption-based asset pricing models with latent state variables. First, we measure how consumption, dividends, and prices depend on Markovian state variables describing aggregate output growth. Subsequently, we identify state-dependent components in the stochastic discount factor using the Euler equation. We develop tractable algorithms for filtering, smoothing, and sieve maximum likelihood estimation, and…

概率聚类的广义贝叶斯框架AI 解读

Summary Loss-based clustering methods, such as k-means clustering and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on mixture models provides an alternative approach, but such methods face computational problems and are highly sensitive to the choice of kernel. In this article we propose a generalized Bayes framework that bridges…

多元线性回归中的高维方差分析AI 解读

Summary In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate…

空间混杂的谱域调整AI 解读

Summary Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. We derive necessary conditions on the coherence between the exposure and the unmeasured confounder that ensure the effect of exposure is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. One assumption that ensures…

群组效应异质性与干扰下的时变因果效应调节AI 解读

Summary The micro-randomized trial is a sequential randomized experimental design to empirically evaluate the effectiveness of mobile health intervention components that may be delivered at hundreds or thousands of decision points. Micro-randomized trials have motivated a new class of causal estimands, termed causal excursion effects, for which semiparametric inference can be conducted via a weighted, centred least-squares criterion (Boruvka et al., 2018). Causal excursion…

变量消除、图约简与有效 g 公式AI 解读

Summary We study efficient estimation of an interventional mean associated with a point exposure treatment under a causal graphical model represented by a directed acyclic graph without hidden variables. Under such a model, a subset of the variables may be uninformative, in that failure to measure them neither precludes identification of the interventional mean nor changes the semiparametric variance bound for regular estimators of it. We develop a set of graphical criteria…

多元区间删失数据的边际比例风险模型AI 解读

Summary Multivariate interval-censored data arise when there are multiple types of events or clusters of study subjects, such that the event times are potentially correlated and when each event is only known to occur over a particular time interval. We formulate the effects of potentially time-varying covariates on the multivariate event times through marginal proportional hazards models while leaving the dependence structures of the related event times unspecified. We…

稀疏网络中社区数量的估计AI 解读

Among the nonparametric methods of estimating the number of communities (K) in a community detection problem, methods based on the spectrum of the Bethe Hessian matrices (Hζ with the scalar parameter ζ) have garnered much popularity for their simplicity, computational efficiency, and robustness to the sparsity of data. For certain heuristic choices of ζ, such methods have been shown to be consistent for networks with N nodes with a common expected degree of ω( log N). In…

时变极值依赖结构的统计推断AI 解读

We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and of the spectral measures integrated over time. The uniform asymptotic normality of these estimators is proved under suitable nonparametric smoothness and regularity assumptions. We then use the process convergence of the integrated spectral…