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Ogburn 等对《广义线性模型参数的弱假设推断》的讨论AI 解读

Not all conditional associations between outcomes and exposures are of interest. Those that are tend to be directional: up or down. The simplest way to assess directionality is to fit a confounder- adjusted linear exposure term, as the authors propose. We agree with this approach as some of us have argued that linear slopes are meaningful and interpretable even if the directional association is not linear (Buja et al., 2019, section 10). The authors, and Whitney et al.…

Lavine 与 Hodges 对《广义线性模型参数的弱假设推断》的讨论AI 解读

The authors advocate a style and rhetoric of statistical analysis that begins with specifying an estimand and ends with an estimate and interval. They say, ‘The starting point… is to come up with an estimand that is meaningful when the above [generalized partially linear] model [(4)] does not hold, but reduces to [the familiar regression coefficient] β when the model holds; this… allows for nonparametric inference to be developed for that estimand’. However, in our opinion,…

Kuldeep Kumar 对《广义线性模型参数的弱假设推断》的讨论AI 解读

According to Leo Breiman (2001), there are two broad cultures for analysing and modelling to reach conclusions from the data. The first one is data modelling culture where the value of the parameters are estimated from the data and then the model is used for information and/or prediction. The second one is algorithmic modelling culture, where the approach is to find a function f(x) using an algorithm that operates on x to predict y. In the first case, statistical tools like…

Ian Hunt 对《广义线性模型参数的少假设推断》的讨论AI 解读

This paper offers a generic and principled addition to conventional statistical modelling. It is a real advance in applicable methodology. But there is no need in the paper for the following claims: that statisticians routinely use ‘dishonest’ modelling assumptions, that statisticians should aim for ‘purely evidence-based’ inferences and that modelling assumptions are ‘almost always a pure mathematical convenience’. These sorts of claims are redundant or misleading for three…

董朝华、高继挺与 Oliver Linton 对《广义线性模型参数的弱假设推断》的讨论AI 解读

The title of this paper is ironically self-fulfilling, since there are almost no meaningful assumptions made throughout! The starting point is that we have some plausible semi-parametric model, which is a special case of a more general non-parametric model, but we wish to allow for misspecification and in particular define an estimand that is meaningful in the non-parametric model and that specialises in the plausible model to a slope coefficient. However, since the…

Blair Bilodeau 对“广义线性模型参数的弱假设推断”的讨论AI 解读

I commend Vansteelandt and Dukes for (a) advocating that statistics move beyond well-specified assumptions and (b) providing a practical estimator to address this for generalised linear models (GLMs). Furthermore, their derivation of theoretical guarantees for this estimator is highly attractive. However, the theorem assumptions exclude many standard machine learning methods, which may violate the spirit of ‘assumption-lean’ inference guarantees. Theorems 2 and 4 assume that…

Pallavi Basu 对《广义线性模型参数的弱假设推断》的讨论AI 解读

The authors propose an ingenious way to improve on providing inference for the main and interaction effects for generalised linear model parameters. With the use of the efficient influence function, they can extend the allowable bias introduced by machine learning estimators up to op(n −1/4). Noting that cross-fitting has been suggested to counter the Donsker condition, it may be a useful alternative to contrast with machine learning estimates, averages over sample splits or…

Hennig 对《广义线性模型参数的弱假设推断》的讨论AI 解读

There is a tendency in statistics to talk about model assumptions in a misleading way. Most of us probably agree with George Box's ‘all models are wrong but some are useful’, yet there is much communication that implies that for applying methods ‘assuming’ certain models, these models have to be true. If this were so, no model-based method could ever be used! Generally model assumptions do not have to be fulfilled. A model assumption just means that certain theoretical…

Heather Battey 对《广义线性模型参数的弱假设推断》的讨论AI 解读

For situations in which there is uncertainty over the underlying probabilistic model, there are at least three broad approaches. One is to seek reliable inference for interest parameters or perhaps, as the authors advocate, for quantities retaining at least a degree of interpretability under misspecification. Another is to acknowledge more explicitly the model uncertainty. A third approach, loosely connected to the first, is to encapsulate uncertainty over the model in a…

Stensrud 与 Sarvet 对《广义线性模型参数的弱假设推断》的讨论AI 解读

We congratulate Vansteelandt and Dukes (V & D) with their innovative and interesting article. Here we further explore the interpretation of V & D’s main effects estimand. An algorithm for causal inference. There has been tremendous progress in causal inference by approaching causal queries in the following way (Hernan & Robins, 2020; Richardson & Robins, 2013; Robins, 1986): Choose a causal target: an estimand that corresponds to a scientific question of interest (usually a…

《广义线性模型参数的弱假设推断》讨论与致谢附议AI 解读

In my view, one of the most important contributions of the field of causal inference has been to place the target of inference, the desired estimand, at the centre of the analysis. The estimand is chosen in view of the research question, and typically reflects what decision problem we need to solve or what our ideal (target) trial would be. Crucially, the (causal) estimand is not automatically a parameter that happens to parametrise a chosen model. The role of models is…

广义线性模型参数的弱假设推断AI 解读

Abstract Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive model selection process, which may induce excess uncertainty that is not usually acknowledged. Moreover, the assumptions encoded in the chosen model rarely represent some a priori known, ground truth, making standard inferences…

异质缺失下的高维变点估计AI 解读

Abstract We propose a new method for changepoint estimation in partially observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a ‘MissCUSUM’ transformation (a generalisation of the popular cumulative sum statistics), that captures the interaction between the signal strength and the level of missingness in each coordinate. In order to borrow strength across the…

具有多重不连续点的函数型过程AI 解读

Abstract We consider the problem of estimating multiple change points for a functional data process. There are numerous examples in science and finance in which the process of interest may be subject to some sudden changes in the mean. The process data that are not in a close vicinity of any change point can be analysed by the usual nonparametric smoothing methods. However, the data close to change points and contain the most pertinent information of structural breaks need…

Abstract Modern high-dimensional methods often adopt the ‘bet on sparsity’ principle, while in supervised multivariate learning statisticians may face ‘dense’ problems with a large number of nonzero coefficients. This paper proposes a novel clustered reduced-rank learning (CRL) framework that imposes two joint matrix regularizations to automatically group the features in constructing predictive factors. CRL is more interpretable than low-rank modelling and relaxes the…

用于评估重复研究成功的怀疑贝叶斯因子AI 解读

Abstract Replication studies are increasingly conducted but there is no established statistical criterion for replication success. We propose a novel approach combining reverse-Bayes analysis with Bayesian hypothesis testing: a sceptical prior is determined for the effect size such that the original finding is no longer convincing in terms of a Bayes factor. This prior is then contrasted to an advocacy prior (the reference posterior of the effect size based on the original…

高维经验贝叶斯主成分分析AI 解读

Abstract When the dimension of data is comparable to or larger than the number of data samples, principal components analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an empirical Bayes PCA method that reduces this noise by estimating a joint prior distribution for the principal components. EB-PCA is based on the classical Kiefer–Wolfowitz non-parametric maximum likelihood estimator for empirical Bayes estimation, distributional results…

多个因果有序中介变量下的因果中介分析半参数估计AI 解读

Abstract Causal mediation analysis concerns the pathways through which a treatment affects an outcome. While most of the mediation literature focuses on settings with a single mediator, a flourishing line of research has examined settings involving multiple mediators, under which path-specific effects (PSEs) are often of interest. We consider estimation of PSEs when the treatment effect operates through K(≥ 1) causally ordered, possibly multivariate mediators. In this…

无限时域强化学习中价值函数的统计推断AI 解读

Abstract Reinforcement learning is a general technique that allows an agent to learn an optimal policy and interact with an environment in sequential decision-making problems. The goodness of a policy is measured by its value function starting from some initial state. The focus of this paper was to construct confidence intervals (CIs) for a policy’s value in infinite horizon settings where the number of decision points diverges to infinity. We propose to model the…

条件矩模型的贝叶斯估计与比较AI 解读

Abstract We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The non-parametric exponentially tilted empirical likelihood function is constructed to satisfy a sequence of unconditional moments based on an increasing (in sample size) vector of approximating functions (such as tensor splines based on the splines of each conditioning variable). For any given sample size,…

基于相关矩阵的主成分分析的渐近性质AI 解读

It is a common practice to conduct principal component analysis (PCA) using standardized data, which is equivalent to applying PCA to the correlation matrix rather than the covariance matrix. Yet little research has been done about such differences in the context of high frequency data. This paper bridges this gap. We derive the analytical forms of the asymptotic biases and variances for the estimators of the integrated eigenvalues and eigenvectors. Furthermore, we propose a…

含局部因子的因子模型：相关因子数量的确定AI 解读

We extend the theory on factor models by incorporating “local” factors into the model. Local factors affect only an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. We derive which factors are pervasive enough to be economically important and which factors are pervasive enough to be estimable using the common principal component estimator. We then introduce a new class of…

多因子误差结构下异质空间面板的估计与推断AI 解读

We develop a unifying econometric framework for the analysis of heterogeneous panel data models that can account for both spatial dependence and common factors. To tackle the challenging issues of endogeneity due to the spatial lagged term and the correlation between the regressors and factors, we propose the CCEX-IV estimation procedure that approximates factors by the cross-section averages of regressors and deals with the spatial endogeneity using the internal…

共同冲击面板中免受附带参数问题影响的推断方法AI 解读

This paper develops a novel Method of Moments approach for panel data models with endogenous regressors and unobserved common factors. The proposed approach does not require estimating explicitly a large number of parameters in either time-series or cross-sectional dimension, T and N respectively. Hence, it is free from the incidental parameter problem. In particular, the proposed approach does not suffer from “Nickell bias” of order O(T−1), nor from bias terms that are of…