Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics

• URL: http://arxiv.org/abs/2408.06103v1
• Date: Mon, 12 Aug 2024 12:43:30 GMT
• Title: Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics
• Authors: Xingyu Chen, Lin Liu, Rajarshi Mukherjee,
• Abstract summary: We consider the estimation of regression coefficients and signal-to-noise ratio in high-dimensional Generalized Linear Models (GLMs) We derive Consistent and Asymptotically Normal (CAN) estimators of our targets of inference. We complement our theoretical results with numerical experiments and comparisons with existing literature.
• Score: 30.324051162373973
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we consider the estimation of regression coefficients and signal-to-noise (SNR) ratio in high-dimensional Generalized Linear Models (GLMs), and explore their implications in inferring popular estimands such as average treatment effects in high-dimensional observational studies. Under the ``proportional asymptotic'' regime and Gaussian covariates with known (population) covariance $\Sigma$, we derive Consistent and Asymptotically Normal (CAN) estimators of our targets of inference through a Method-of-Moments type of estimators that bypasses estimation of high dimensional nuisance functions and hyperparameter tuning altogether. Additionally, under non-Gaussian covariates, we demonstrate universality of our results under certain additional assumptions on the regression coefficients and $\Sigma$. We also demonstrate that knowing $\Sigma$ is not essential to our proposed methodology when the sample covariance matrix estimator is invertible. Finally, we complement our theoretical results with numerical experiments and comparisons with existing literature.

Related papers

• Statistical Inference in Classification of High-dimensional Gaussian Mixture [1.2354076490479515]
  We investigate the behavior of a general class of regularized convex classifiers in the high-dimensional limit. Our focus is on the generalization error and variable selection properties of the estimators.
  arXiv  Detail & Related papers  (2024-10-25T19:58:36Z)
• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Analysis of Bootstrap and Subsampling in High-dimensional Regularized Regression [29.57766164934947]
  We investigate popular resampling methods for estimating the uncertainty of statistical models. We provide a tight description of the biases and variances estimated by these methods in the context of generalized linear models.
  arXiv  Detail & Related papers  (2024-02-21T08:50:33Z)
• Algebraic and Statistical Properties of the Ordinary Least Squares Interpolator [3.4320157633663064]
  We provide results for the minimum $ell$-norm OLS interpolator. We present statistical results such as an extension of the Gauss-Markov theorem. We conduct simulations that further explore the properties of the OLS interpolator.
  arXiv  Detail & Related papers  (2023-09-27T16:41:10Z)
• Adaptive Linear Estimating Equations [5.985204759362746]
  In this paper, we propose a general method for constructing debiased estimator. It makes use of the idea of adaptive linear estimating equations, and we establish theoretical guarantees of normality. A salient feature of our estimator is that in the context of multi-armed bandits, our estimator retains the non-asymptotic performance.
  arXiv  Detail & Related papers  (2023-07-14T12:55:47Z)
• Noise Estimation in Gaussian Process Regression [1.5002438468152661]
  The presented method can be used to estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. We demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.
  arXiv  Detail & Related papers  (2022-06-20T19:36:03Z)
• Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
  We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. We establish non-asymptotic bounds for both the operator defect and the estimation error.
  arXiv  Detail & Related papers  (2022-01-21T02:46:57Z)
• Nonconvex Stochastic Scaled-Gradient Descent and Generalized Eigenvector Problems [98.34292831923335]
  Motivated by the problem of online correlation analysis, we propose the emphStochastic Scaled-Gradient Descent (SSD) algorithm. We bring these ideas together in an application to online correlation analysis, deriving for the first time an optimal one-time-scale algorithm with an explicit rate of local convergence to normality.
  arXiv  Detail & Related papers  (2021-12-29T18:46:52Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• On the Double Descent of Random Features Models Trained with SGD [78.0918823643911]
  We study properties of random features (RF) regression in high dimensions optimized by gradient descent (SGD) We derive precise non-asymptotic error bounds of RF regression under both constant and adaptive step-size SGD setting. We observe the double descent phenomenon both theoretically and empirically.
  arXiv  Detail & Related papers  (2021-10-13T17:47:39Z)
• Heavy-tailed Streaming Statistical Estimation [58.70341336199497]
  We consider the task of heavy-tailed statistical estimation given streaming $p$ samples. We design a clipped gradient descent and provide an improved analysis under a more nuanced condition on the noise of gradients.
  arXiv  Detail & Related papers  (2021-08-25T21:30:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.