The empirical median for estimating the common mean of heteroscedastic random variables

• URL: http://arxiv.org/abs/2501.16956v1
• Date: Tue, 28 Jan 2025 13:57:54 GMT
• Title: The empirical median for estimating the common mean of heteroscedastic random variables
• Authors: Sirine Louati,
• Abstract summary: We study the problem of mean estimation in the heteroscedastic setting.<n>We establish upper and lower bounds on its estimation error that are of the same order.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of mean estimation in the heteroscedastic setting. In particular, we consider symmetric random variables having the same location parameter and different and unknown scale parameters. Our goal is then to estimate their unknown common location parameter. It is an elementary topic but yet a not very well-studied one since we always make the assumption that the random variables are independent and identically distributed. In this paper, we study the median estimator and we establish upper and lower bounds on its estimation error that are of the same order and that generalize and improve recent results of Devroye et al. and Xia.

Related papers

• When three experiments are better than two: Avoiding intractable correlated aleatoric uncertainty by leveraging a novel bias--variance tradeoff [1.1609229408259252]
  Real-world experimental scenarios are characterized by the presence of heteroskedastic aleatoric uncertainty.<n>We propose novel active learning strategies that directly reduce the bias between experimental rounds.
  arXiv  Detail & Related papers  (2025-09-04T16:23:54Z)
• Bias and Identifiability in the Bounded Confidence Model [4.660328753262075]
  bounded confidence models describe how a population can reach consensus, fragmentation, or polarization.<n> estimation of model parameters is a key aspect, and maximum likelihood estimation provides a principled way to tackle it.<n>Our results show how the analysis of the likelihood function is a fruitful approach for better understanding the pitfalls and possibilities of estimating the parameters of opinion dynamics models.
  arXiv  Detail & Related papers  (2025-06-13T13:04:29Z)
• In-Context Parametric Inference: Point or Distribution Estimators? [66.22308335324239]
  We show that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems.<n>Our experiments indicate that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems.
  arXiv  Detail & Related papers  (2025-02-17T10:00:24Z)
• 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)
• Transformer-based Parameter Estimation in Statistics [0.0]
  We propose a transformer-based approach to parameter estimation. It does not even require knowing the probability density function, which is needed by numerical methods. It is shown that our approach achieves similar or better accuracy as measured by mean-square-errors.
  arXiv  Detail & Related papers  (2024-02-28T04:30:41Z)
• On the Properties and Estimation of Pointwise Mutual Information Profiles [49.877314063833296]
  The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. We introduce a novel family of distributions, Bend and Mix Models, for which the profile can be accurately estimated using Monte Carlo methods.
  arXiv  Detail & Related papers  (2023-10-16T10:02:24Z)
• Conformal inference for regression on Riemannian Manifolds [49.7719149179179]
  We investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space. We prove the almost sure convergence of the empirical version of these regions on the manifold to their population counterparts.
  arXiv  Detail & Related papers  (2023-10-12T10:56:25Z)
• Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement [0.562479170374811]
  Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. We address this problem by considering an order based on (sets of) expectations of random variables mapping into such non-standard spaces. This order contains dominance and expectation order as extreme cases when no, or respectively perfect, cardinal structure is given.
  arXiv  Detail & Related papers  (2023-06-22T11:02:18Z)
• Beyond Normal: On the Evaluation of Mutual Information Estimators [52.85079110699378]
  We show how to construct a diverse family of distributions with known ground-truth mutual information. We provide guidelines for practitioners on how to select appropriate estimator adapted to the difficulty of problem considered.
  arXiv  Detail & Related papers  (2023-06-19T17:26:34Z)
• Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares [47.83169780113135]
  We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. We evaluate our approach on synthetic, as well as the KITTI and EuRoC real-world datasets.
  arXiv  Detail & Related papers  (2023-05-16T15:21:09Z)
• Benchmarking common uncertainty estimation methods with histopathological images under domain shift and label noise [62.997667081978825]
  In high-risk environments, deep learning models need to be able to judge their uncertainty and reject inputs when there is a significant chance of misclassification. We conduct a rigorous evaluation of the most commonly used uncertainty and robustness methods for the classification of Whole Slide Images. We observe that ensembles of methods generally lead to better uncertainty estimates as well as an increased robustness towards domain shifts and label noise.
  arXiv  Detail & Related papers  (2023-01-03T11:34:36Z)
• Predicting Out-of-Domain Generalization with Neighborhood Invariance [59.05399533508682]
  We propose a measure of a classifier's output invariance in a local transformation neighborhood. Our measure is simple to calculate, does not depend on the test point's true label, and can be applied even in out-of-domain (OOD) settings. In experiments on benchmarks in image classification, sentiment analysis, and natural language inference, we demonstrate a strong and robust correlation between our measure and actual OOD generalization.
  arXiv  Detail & Related papers  (2022-07-05T14:55:16Z)
• Nonparametric Conditional Local Independence Testing [69.31200003384122]
  Conditional local independence is an independence relation among continuous time processes. No nonparametric test of conditional local independence has been available. We propose such a nonparametric test based on double machine learning.
  arXiv  Detail & Related papers  (2022-03-25T10:31:02Z)
• Random Forest Weighted Local Fréchet Regression with Random Objects [18.128663071848923]
  We propose a novel random forest weighted local Fr'echet regression paradigm. Our first method uses these weights as the local average to solve the conditional Fr'echet mean. Second method performs local linear Fr'echet regression, both significantly improving existing Fr'echet regression methods.
  arXiv  Detail & Related papers  (2022-02-10T09:10:59Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Reducing the Variance of Variational Estimates of Mutual Information by Limiting the Critic's Hypothesis Space to RKHS [0.0]
  Mutual information (MI) is an information-theoretic measure of dependency between two random variables. Recent methods realize parametric probability distributions or critic as a neural network to approximate unknown density ratios. We argue that the high variance characteristic is due to the uncontrolled complexity of the critic's hypothesis space.
  arXiv  Detail & Related papers  (2020-11-17T14:32:48Z)
• Distributionally Robust Local Non-parametric Conditional Estimation [22.423052432220235]
  We propose a new distributionally robust estimator that generates non-parametric local estimates. We show that despite being generally intractable, the local estimator can be efficiently found via convex optimization. Experiments with synthetic and MNIST datasets show the competitive performance of this new class of estimators.
  arXiv  Detail & Related papers  (2020-10-12T00:11:17Z)
• Bayesian parameter estimation using Gaussian states and measurements [0.0]
  We consider three paradigmatic estimation schemes in continuous-variable quantum metrology. We investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization.
  arXiv  Detail & Related papers  (2020-09-08T12:54:12Z)
• Minimax Optimal Estimation of KL Divergence for Continuous Distributions [56.29748742084386]
  Esting Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor between these samples.
  arXiv  Detail & Related papers  (2020-02-26T16:37:37Z)
• GenDICE: Generalized Offline Estimation of Stationary Values [108.17309783125398]
  We show that effective estimation can still be achieved in important applications. Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions. The resulting algorithm, GenDICE, is straightforward and effective.
  arXiv  Detail & Related papers  (2020-02-21T00:27:52Z)
• Propose, Test, Release: Differentially private estimation with high probability [9.25177374431812]
  We introduce a new general version of the PTR mechanism that allows us to derive high probability error bounds for differentially private estimators. Our algorithms provide the first statistical guarantees for differentially private estimation of the median and mean without any boundedness assumptions on the data.
  arXiv  Detail & Related papers  (2020-02-19T01:29:05Z)
• Estimating Gradients for Discrete Random Variables by Sampling without Replacement [93.09326095997336]
  We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement. We show that our estimator can be derived as the Rao-Blackwellization of three different estimators.
  arXiv  Detail & Related papers  (2020-02-14T14:15:18Z)

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.