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1. Inference for Iterated GMM Under Misspecification

   https://doi.org/10.3982/ECTA16274  

   Hansen, Bruce E.; Lee, Seojeong (January 2021, Econometrica)

   null (Ed.)

   This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008). 

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2. More robust estimation of average treatment effects using kernel optimal matching in an observational study of spine surgical interventions

   https://doi.org/10.1002/sim.8904  

   Kallus, Nathan; Pennicooke, Brenton; Santacatterina, Michele (May 2021, Statistics in Medicine)

   Inverse probability of treatment weighting (IPTW), which has been used to estimate average treatment effects (ATE) using observational data, tenuously relies on the positivity assumption and the correct specification of the treatment assignment model, both of which are problematic assumptions in many observational studies. Various methods have been proposed to overcome these challenges, including truncation, covariate‐balancing propensity scores, and stable balancing weights. Motivated by an observational study in spine surgery, in which positivity is violated and the true treatment assignment model is unknown, we present the use of optimal balancing by kernel optimal matching (KOM) to estimate ATE. By uniformly controlling the conditional mean squared error of a weighted estimator over a class of models, KOM simultaneously mitigates issues of possible misspecification of the treatment assignment model and is able to handle practical violations of the positivity assumption, as shown in our simulation study. Using data from a clinical registry, we apply KOM to compare two spine surgical interventions and demonstrate how the result matches the conclusions of clinical trials that IPTW estimates spuriously refute. 

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3. DiffPoseNet: Direct Differentiable Camera Pose Estimation

   Parameshwara, Chethan M.; Hari, Gokul; Fermuller, Cornelia; Sanket, Nitin; Aloimonos, Yiannis (January 2022, IEEE Conference on Computer Vision and Pattern Recognition)

   Current deep neural network approaches for camera pose estimation rely on scene structure for 3D motion estimation, but this decreases the robustness and thereby makes cross-dataset generalization difficult. In contrast, classical approaches to structure from motion estimate 3D motion utilizing optical flow and then compute depth. Their accuracy, however, depends strongly on the quality of the optical flow. To avoid this issue, direct methods have been proposed, which separate 3D motion from depth estimation, but compute 3D motion using only image gradients in the form of normal flow. In this paper, we introduce a network NFlowNet, for normal flow estimation which is used to enforce robust and direct constraints. In particular, normal flow is used to estimate relative camera pose based on the cheirality (depth positivity) constraint. We achieve this by formulating the optimization problem as a differentiable cheirality layer, which allows for end-to-end learning of camera pose. We perform extensive qualitative and quantitative evaluation of the proposed DiffPoseNet’s sensitivity to noise and its generalization across datasets. We compare our approach to existing state-of-the-art methods on KITTI, TartanAir, and TUM-RGBD datasets. 

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4. Dynamical Gaussian, lognormal, and reverse lognormal maximum‐likelihood ensemble filter

   https://doi.org/10.1002/qj.4706  

   Van_Loon, Senne; Fletcher, Steven J; Zupanski, Milija (April 2024, Quarterly Journal of the Royal Meteorological Society)

   We present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve. 

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5. Improved Spectral Density Estimation via Explicit and Implicit Deflation

   Bhattacharjee, Rajarshi; Jayaram, Rajesh; Musco, Cameron; Musco, Christopher; Ray, Archan (January 2025, ACM-SIAM Symposium on Discrete Algorithms)

   We study algorithms for approximating the spectral density (i.e., the eigenvalue distribution) of a symmetric matrix A ∈ ℝn×n that is accessed through matrix-vector product queries. Recent work has analyzed popular Krylov subspace methods for this problem, showing that they output an ∈ · || A||2 error approximation to the spectral density in the Wasserstein-1 metric using O (1/∈ ) matrix-vector products. By combining a previously studied Chebyshev polynomial moment matching method with a deflation step that approximately projects off the largest magnitude eigendirections of A before estimating the spectral density, we give an improved error bound of ∈ · σℓ (A) using O (ℓ log n + 1/∈ ) matrix-vector products, where σℓ (A) is the ℓth largest singular value of A. In the common case when A exhibits fast singular value decay and so σℓ (A) « ||A||2, our bound can be much stronger than prior work. We also show that it is nearly tight: any algorithm giving error ∈ · σℓ (A) must use Ω(ℓ + 1/∈ ) matrix-vector products. We further show that the popular Stochastic Lanczos Quadrature (SLQ) method essentially matches the above bound for any choice of parameter ℓ, even though SLQ itself is parameter-free and performs no explicit deflation. Our bound helps to explain the strong practical performance and observed ‘spectrum adaptive’ nature of SLQ, and motivates a simple variant of the method that achieves an even tighter error bound. Technically, our results require a careful analysis of how eigenvalues and eigenvectors are approximated by (block) Krylov subspace methods, which may be of independent interest. Our error bound for SLQ leverages an analysis of the method that views it as an implicit polynomial moment matching method, along with recent results on low-rank approximation with single-vector Krylov methods. We use these results to show that the method can perform ‘implicit deflation’ as part of moment matching. 

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