Universal inference

Wasserman, Larry; Ramdas, Aaditya; Balakrishnan, Sivaraman

doi:10.1073/pnas.1922664117

Cited by 112 publications

(104 citation statements)

References 40 publications

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“…2. Universal confidence intervals are guaranteed to coverψ KL,k (θ ) at the nominal rate for any sample size n under the conditions of Proposition 7 in Wasserman, Ramdas and Balakrishnan (2020). However, we will show that the length of the confidence interval is of order θ KL,k −θ KL,k , 9 which is generically n −1/2 when n > k n 1/2 .…”

Section: On Universal Inferencementioning

confidence: 73%

Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning

Liu¹,

Mukherjee²,

Robins³

2020

Statist. Sci.

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We thank the editors for this opportunity and the discussants Kennedy, Balakrishnan and Wasserman (2020) (abbreviated as KBW in the sequel) for their insightful commentaries on our paper (Liu, Mukherjee and Robins, 2020) (abbreviated as LMR in the sequel). A BRIEF INTRODUCTION TO HIGHER ORDER INFLUENCE FUNCTIONSWe would like to start our rejoinder by responding to the philosophical comments in Section 6 of KBW's discussion before getting into the other more technical comments. In Section 6, KBW divide statistical procedures into structure-driven and methods-driven but also acknowledge that the boundary between these two categories is blurry. For example, even for the poster child of the methods-driven tools -deep neural networks -one common research direction is to prove some form of optimality or robustness under some assumptions, often quantified by smoothness, sparsity or other related complexity measures such as metric entropy (Schmidt-Hieber, 2020, Hayakawa and Suzuki, 2020, Barron and Klusowski, 2018.The discussants then state that higher order influence function (HOIF) based methods are 'structure-driven' because 'they typically rely on carefully constructed series estimates' and achieve 'better performance over appropriate Hölder spaces potentially at the expense of being more structure driven.' This statement misunderstands the motivation and goals of HOIF estimation. Our goal has always been to make HOIF fully methods-driven. However,

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Section: On Universal Inferencementioning

confidence: 73%

Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning

Liu¹,

Mukherjee²,

Robins³

2020

Statist. Sci.

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“…On the other hand, Monte Carlo simulation of the asymptotic distribution in Theorem 2 is computationally much easier, even though there are still optimizations to be solved. Another method is the split likelihood ratio test recently proposed by Wasserman et al (2020) that is computationally fast and does not suffer from singularity or boundary issues. By making use of a sample splitting trick, this split LRT is able to control the type I error at any pre-specified level.…”

Section: Discussionmentioning

confidence: 99%

“…Another method is the split likelihood ratio test recently proposed by Wasserman et al. ( 2020 ) that is computationally fast and does not suffer from singularity or boundary issues. By making use of a sample splitting trick, this split LRT is able to control the type I error at any pre-specified level.…”

Section: Discussionmentioning

confidence: 99%

A Note on Likelihood Ratio Tests for Models with Latent Variables

2020

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The likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks’ theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the restricted model, a $$\chi ^2$$ χ 2 distribution with degrees of freedom equal to the difference in the number of free parameters between the two nested models under comparison. For models with latent variables such as factor analysis, structural equation models and random effects models, however, it is often found that the $$\chi ^2$$ χ 2 approximation does not hold. In this note, we show how the regularity conditions of Wilks’ theorem may be violated using three examples of models with latent variables. In addition, a more general theory for LRT is given that provides the correct asymptotic theory for these LRTs. This general theory was first established in Chernoff (J R Stat Soc Ser B (Methodol) 45:404–413, 1954) and discussed in both van der Vaart (Asymptotic statistics, Cambridge, Cambridge University Press, 2000) and Drton (Ann Stat 37:979–1012, 2009), but it does not seem to have received enough attention. We illustrate this general theory with the three examples.

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“…A selection of correct distribution for gathered data sets is an important task. Appropriate methods exist to establish confidence sets and perform hypothesis tests, including an universal procedure [36]. In this regard we should mention that a substantial portion of our data sets is satisfactorily modeled by the three-…”

Section: Maximal Supported Load and Minimal Number Of Reliable Unitsmentioning

confidence: 99%

Spreading of Failures in Small-World Networks: A Connectivity-Dependent Load Sharing Fibre Bundle Model

Domański

2020

Front. Phys.

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A rich variety of multicomponent systems operating under parallel loading may be mapped on and then examined by employing a family of the Fiber Bundle Models. As an example, we consider a system composed of N immobile units located in nodes of a network G and subjected to a growing external load F imposed uniformly on the units. Each unit, characterized by a load threshold δ, is classified as reliable or irreversibly failed, depending on whether δ is bigger, or respectively smaller, than the load felt by the unit. A pair of interdependent units is uniquely indicated by an edge of G. Initially all the units are reliable. When a unit fails, its load is distributed locally among interdependent neighbors if they are reliable, or is otherwise shared globally by all the reliable units. Because of the growing F and the loads that are transferred according to such a seesaw switch between the local and global sharing rules (sLGS), a set of nodes, that holds the reliable units, evolves as G → ∅. During the evolution, a subset G c ⊂ G emerges that represents the limiting state of the system's functionality when the smallest group of n c reliable units sustains the highest load F c. We concentrate on how the Fiber Bundle Model and switching Local-Global-Sharing conspire to drive the system toward G c. Specifically, we assume that {δ} G are quenched-random quantities distributed uniformly over (0, 1) or governed by the Weibull distribution and networks G are the Watts-Strogatz "small-world" graphs with the rewiring probability p that characterizes possible rearrangements of edges in G. We have identified a range of values of p, where the mean highest load f c (N) 〈F c 〉/N, supported by reliable units, scales linearly with the average globalclustering coefficient of the host network. Similar scaling holds for 〈n c 〉 and 〈F c /n c 〉. We have also found that in the large N limit f c (N) → f ∞ c > 0, for all values of p and both considered distributions of {δ} G. The symbol 〈. .. 〉 represents averaging over {δ} G and a suitable ensemble of networks {G}.

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Universal inference

Cited by 112 publications

References 40 publications

Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning

Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning

A Note on Likelihood Ratio Tests for Models with Latent Variables

Spreading of Failures in Small-World Networks: A Connectivity-Dependent Load Sharing Fibre Bundle Model

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