论文检索

利用局部球面高效逼近流形AI 解读

Abstract In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on exploiting such approximations in clustering, data compression, and prediction. Most of the literature relies on linear or locally linear approximations. In this article, we propose a simple and general alternative, which instead uses…

多重检验问题的最优与最大最小程序AI 解读

Abstract Multiple testing problems (MTPs) are a staple of modern statistical analysis. The fundamental objective of MTPs is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to controlling an overall measure of false discovery, like family-wise error rate (FWER) or false discovery rate (FDR). In this paper we provide generalizations to MTPs of the optimal Neyman-Pearson test for a single hypothesis. We show that for simple…

MCMC 输出的最优抽稀AI 解读

Abstract The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to ‘burn in’ and removed, while the remainder of the chain is ‘thinned’ if compression is also required. In this paper, we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path…

摘要暂缺

周倪文与郭旭对《广义线性模型参数的少假设推断》的讨论AI 解读

We thank Professors Vansteelandt and Dukes for their innovative and stimulating paper. They introduce a new estimand which reduces to the exposure effect parameter when the (semi)parametric model holds, is generic for continuous or discrete exposure, and still captures conditional association when model assumption fails. We make some additional understanding of the new estimand and introduce a related new estimand. Here we consider the expectation of the ratio. Here β· and…

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…

Richardson 对《广义线性模型参数的弱假设推断》的讨论AI 解读

I congratulate the authors on an interesting and thought provoking contribution to the literature on modelling associations. A particular strength of the approach advocated by the authors is that it may facilitate the estimation of main effects on the relative risk scale, by taking g = log. In contrast, a GLM specification such as (4) with log link presents difficulties owing to the variation dependence between β and ω(·). This dependence, also called non-congeniality, often…

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…

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…

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…

Choi 与 Wong 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 for major advances in the methodology of estimands, in particular assumption-lean reference for the estimands in possibly misspecified generalised linear models. Whereas the simulation studies in Section 6 indeed support the ‘assumption-lean’ claim and the authors’ software in Practice of Epidemiology187 (pp. 1079–1084, 2018) facilitates such inference, the empirical example in Section 7 seems problematic to illustrate applications of 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…

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…