Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations

• URL: http://arxiv.org/abs/2407.08494v1
• Date: Thu, 11 Jul 2024 13:28:34 GMT
• Title: Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations
• Authors: Hajo Holzmann, Alexander Meister,
• Abstract summary: 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.
• Score: 51.000851088730684
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Expected values weighted by the inverse of a multivariate density or, equivalently, Lebesgue integrals of regression functions with multivariate regressors occur in various areas of applications, including estimating average treatment effects, nonparametric estimators in random coefficient regression models or deconvolution estimators in Berkson errors-in-variables models. The frequently used nearest-neighbor and matching estimators suffer from bias problems in multiple dimensions. By using polynomial least squares fits on each cell of the $K^{\text{th}}$-order Voronoi tessellation for sufficiently large $K$, we develop novel modifications of nearest-neighbor and matching estimators which again converge at the parametric $\sqrt n $-rate under mild smoothness assumptions on the unknown regression function and without any smoothness conditions on the unknown density of the covariates. We stress that in contrast to competing methods for correcting for the bias of matching estimators, our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent smoothing parameters. We complement the upper bounds with appropriate lower bounds derived from information-theoretic arguments, which show that some smoothness of the regression function is indeed required to achieve the parametric rate. Simulations illustrate the practical feasibility of the proposed methods.

Related papers

• Semiparametric conformal prediction [79.6147286161434]
  Risk-sensitive applications require well-calibrated prediction sets over multiple, potentially correlated target variables. We treat the scores as random vectors and aim to construct the prediction set accounting for their joint correlation structure. We report desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Variational Bayesian surrogate modelling with application to robust design optimisation [0.9626666671366836]
  Surrogate models provide a quick-to-evaluate approximation to complex computational models. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and dimensionality reduction. We demonstrate intrinsic and robust structural optimisation problems where cost functions depend on a weighted sum of the mean and standard deviation of model outputs.
  arXiv  Detail & Related papers  (2024-04-23T09:22:35Z)
• Nearest Neighbor Sampling for Covariate Shift Adaptation [7.940293148084844]
  We propose a new covariate shift adaptation method which avoids estimating the weights. The basic idea is to directly work on unlabeled target data, labeled according to the $k$-nearest neighbors in the source dataset. Our experiments show that it achieves drastic reduction in the running time with remarkable accuracy.
  arXiv  Detail & Related papers  (2023-12-15T17:28:09Z)
• Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations [0.0]
  Variational mixtures with full-covariance structures suffer from a quadratic growth due to variational parameters with the number of parameters. We propose a method for constructing an initial Gaussian model approximation that can be used to warm-start variational inference.
  arXiv  Detail & Related papers  (2023-07-12T19:30:04Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Nonparametric Quantile Regression: Non-Crossing Constraints and Conformal Prediction [2.654399717608053]
  We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. We establish non-asymptotic upper bounds for the excess risk of the proposed nonparametric quantile regression function estimators. Numerical experiments including simulation studies and a real data example are conducted to demonstrate the effectiveness of the proposed method.
  arXiv  Detail & Related papers  (2022-10-18T20:59:48Z)
• Support estimation in high-dimensional heteroscedastic mean regression [2.28438857884398]
  We consider a linear mean regression model with random design and potentially heteroscedastic, heavy-tailed errors. We use a strictly convex, smooth variant of the Huber loss function with tuning parameter depending on the parameters of the problem. For the resulting estimator we show sign-consistency and optimal rates of convergence in the $ell_infty$ norm.
  arXiv  Detail & Related papers  (2020-11-03T09:46:31Z)
• Nonparametric Score Estimators [49.42469547970041]
  Estimating the score from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. We propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.
  arXiv  Detail & Related papers  (2020-05-20T15:01:03Z)
• SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models [80.22609163316459]
  We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost.
  arXiv  Detail & Related papers  (2020-04-01T11:49:30Z)
• 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.