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赵继伟对《广义线性模型参数的弱假设推断》的讨论AI 解读

First I congratulate Vansteelandt and Dukes for a fascinating and stimulating paper, which I believe will have great impact on the practical data analysis as well as on the application of semiparametric techniques. In applications, any fitted model could be a misspecified model, for example Ê(A|L) converges to E*(A|L)⁠, where E* denotes the expectation that is evaluated under a working model. The similar notations are also used for Cov and Var throughout. Nonetheless, I…

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

Finally, it is worth noting that in the case of identity link, Robins et al. (2008), Li et al. (2011) and Mukherjee et al. (2017) proposed minimax estimators of functional (5) of V&D, which are root-n consistent, asymptotically normal and semiparametric efficient under rate conditions for estimating nuisance functions that are significantly weaker than those of V&D in Theorem 2 (nuisance estimation rate conditions for the theorem are therefore sufficient but not necessary at…

唐彦博对《广义线性模型参数的弱假设推断》的讨论AI 解读

The method proposed by Vansteelandt and Dukes is an interesting combination of non-parametric and machine learning techniques with traditional ideas in statistics. We note in this discussion that the authors' argument is easily extended to obtain a quantitative rate in terms of the quality of the nonparametric conditional mean estimate, and comment on how this may impact a practitioner's choice of the machine learning model used to estimate the conditional mean. However the…

Ilya Shpitser 对《广义线性模型参数的少假设推断》的讨论AI 解读

A hallmark of principled causal inference is being careful and explicit about assumptions underlying data analysis. In their timely paper, the authors, Professor Stijn Vansteelandt and Oliver Dukes, adopt this view to provide a general roadmap for cautious statistical inference about target parameters. The authors distinguish between assumptions made for substantive reasons and those made for convenience. An important feature of their approach is that an estimand with…

Phillips 与 van der Laan 对《广义线性模型参数的弱假设推断》的讨论AI 解读

We commend the authors on this novel non-parametric extension of main and interaction coefficients in a generalised linear model (GLM), such as E(Y|A,L)=βA+g(L)⁠, and their efficient estimation. There is a wealth of non-parametric extensions one could pursue, including weighted squared error projections of a conditional treatment effect E(Y|A=a,L)-E(Y|A=0,L) and conditional interaction effect E(Y|A=(a1+1,a2+1),L)-E(Y|A=(a1,a2+1),L)-E(Y|A=(a1+1,a2),L)+E(Y|A=(a1,a2),L) onto a…

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,…

Hines 与 Diaz-Ordaz 对《广义线性模型参数的弱假设推断》的讨论AI 解读

We congratulate the authors on their work, which contributes to a growing movement in Statistics, moving away from (semi)parametric-based regression model assumptions, in favour of understanding working models as non-parametric projections of the true distribution. Here, we highlight this aspect of the work, and draw connections with other recent developments. The parametric modeller assumes that for some particular β, ω(.), the remainder term is exactly zero. Inference is…

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…

Buja 等对“广义线性模型参数的弱假设推断”的讨论AI 解读

We thank the authors for their stimulating article. At the highest level, it agrees with our thinking as expressed in the second of two articles in Statistical Science (Buja et al., 2019). The guiding principle is to focus on quantities of interest that are meaningful statistical functionals, beyond the statistical models that motivate them, even when those models are fully misspecified. In some form, this focus has existed for decades in the semi-parametric literature. We…

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…

《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…

难处理似然下的稳健广义贝叶斯推断AI 解读

Abstract Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of 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…

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,…

稀疏纵向观测的内蕴黎曼函数型数据分析AI 解读

A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from…

Wasserstein 距离下光滑密度的极小极大估计AI 解读

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates for this problem for general Wasserstein distances for two classes of densities: smooth probability densities on [0,1]d bounded away from 0, and sub-Gaussian densities lying in the Hölder class Cs, s∈(0,1). Unlike classical nonparametric…

多元最大稳定分布贝叶斯推断的一致性AI 解读

Predicting extreme events is important in many applications in risk analysis. Extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction. Although various Bayesian inferential procedures have been proposed in the literature of univariate extremes and some for multivariate extremes, the study of their asymptotic properties has been left largely untouched. In this paper we focus on…

部分线性Cox模型的深度学习方法AI 解读

While deep learning approaches to survival data have demonstrated empirical success in applications, most of these methods are difficult to interpret and mathematical understanding of them is lacking. This paper studies the partially linear Cox model, where the nonlinear component of the model is implemented using a deep neural network. The proposed approach is flexible and able to circumvent the curse of dimensionality, yet it facilitates interpretability of the effects of…