More Like this

1. Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities

   https://doi.org/10.1093/restud/rdae025  

   Chen, Xiaohong; Christensen, Timothy; Kankanala, Sid (March 2024, Review of Economic Studies)

   We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least-squares estimators. When implemented with this choice, estimators of both the structural function h0 and its derivatives (such as elasticities) converge at the fastest possible (i.e. minimax) rates in sup-norm. The second is for constructing uniform confidence bands (UCBs) for h0 and its derivatives. Our UCBs guarantee coverage over a generic class of data-generating processes and contract at the minimax rate, possibly up to a logarithmic factor. As such, our UCBs are asymptotically more efficient than UCBs based on the usual approach of undersmoothing. As an application, we estimate the elasticity of the intensive margin of firm exports in a monopolistic competition model of international trade. Simulations illustrate the good performance of our procedures in empirically calibrated designs. Our results provide evidence against common parameterizations of the distribution of unobserved firm heterogeneity. 

   more » « less
2. Adaptive minimax density estimation on ℝ d for Huber’s contamination model

   https://doi.org/10.1093/imaiai/iaad045  

   Zhang, Peiliang; Ren, Zhao (September 2023, Information and Inference: A Journal of the IMA)

   Abstract We address the problem of adaptive minimax density estimation on $$\mathbb{R}^{d}$$ with $$L_{p}$$ loss functions under Huber’s contamination model. To investigate the contamination effect on the optimal estimation of the density, we first establish the minimax rate with the assumption that the density is in an anisotropic Nikol’skii class. We then develop a data-driven bandwidth selection procedure for kernel estimators, which can be viewed as a robust generalization of the Goldenshluger-Lepski method. We show that the proposed bandwidth selection rule can lead to the estimator being minimax adaptive to either the smoothness parameter or the contamination proportion. When both of them are unknown, we prove that finding any minimax-rate adaptive method is impossible. Extensions to smooth contamination cases are also discussed. 

   more » « less
3. On Bayes factor functions

   Datta, Saptati; Guha, Riana; Shudde, Rachael; Johnson, Valen E (June 2025, arXiv: arXiv:2506.16674)

   We describe Bayes factors functions based on the sampling distributions of z, t, χ2, and F statistics, using a class of inverse-moment prior distributions to define alternative hypotheses. These non-local alternative prior distributions are centered on standardized effects, which serve as indices for the Bayes factor function. We compare the conclusions drawn from resulting Bayes factor functions to those drawn from Bayes factors defined using local alternative prior specifications and examine their frequentist operating characteristics. Finally, an application of Bayes factor functions for replicated experimental designs in psychology are provided. 

   more » « less
4. A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family

   Banerjee, Trambak; Liu, Qiang; Mukherjee, Gourab; Sun, Wenguang (January 2020, Journal of machine learning research)

   null (Ed.)

   We develop a Nonparametric Empirical Bayes (NEB) framework for compound estimation in the discrete linear exponential family, which includes a wide class of discrete distributions frequently arising from modern big data applications. We propose to directly estimate the Bayes shrinkage factor in the generalized Robbins' formula via solving a scalable convex program, which is carefully developed based on a RKHS representation of the Stein's discrepancy measure. The new NEB estimation framework is flexible for incorporating various structural constraints into the data driven rule, and provides a unified approach to compound estimation with both regular and scaled squared error losses. We develop theory to show that the class of NEB estimators enjoys strong asymptotic properties. Comprehensive simulation studies as well as analyses of real data examples are carried out to demonstrate the superiority of the NEB estimator over competing methods. 

   more » « less
5. Estimating location parameters in sample-heterogeneous distributions

   https://doi.org/10.1093/imaiai/iaab013  

   Pensia, Ankit; Jog, Varun; Loh, Po-Ling (June 2021, Information and Inference: A Journal of the IMA)

   null (Ed.)

   Abstract Estimating the mean of a probability distribution using i.i.d. samples is a classical problem in statistics, wherein finite-sample optimal estimators are sought under various distributional assumptions. In this paper, we consider the problem of mean estimation when independent samples are drawn from $$d$$-dimensional non-identical distributions possessing a common mean. When the distributions are radially symmetric and unimodal, we propose a novel estimator, which is a hybrid of the modal interval, shorth and median estimators and whose performance adapts to the level of heterogeneity in the data. We show that our estimator is near optimal when data are i.i.d. and when the fraction of ‘low-noise’ distributions is as small as $$\varOmega \left (\frac{d \log n}{n}\right )$$, where $$n$$ is the number of samples. We also derive minimax lower bounds on the expected error of any estimator that is agnostic to the scales of individual data points. Finally, we extend our theory to linear regression. In both the mean estimation and regression settings, we present computationally feasible versions of our estimators that run in time polynomial in the number of data points. 

   more » « less