Nonparametric Regression under Cluster Sampling

Yuya Shimizu

Home/Archive/arXiv

arXiv · 2403.04766

Nonparametric Regression under Cluster Sampling

Yuya Shimizu

View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our theory accommodates growing and heterogeneous cluster sizes. We derive asymptotic conditional bias and variance, establish uniform consistency, and prove asymptotic normality. Our findings reveal that under heterogeneous cluster sizes, the asymptotic variance includes a new term reflecting within-cluster dependence, which is overlooked when cluster sizes are presumed to be bounded. We propose valid approaches for bandwidth selection and inference, introduce estimators of the asymptotic variance, and demonstrate their consistency. In simulations, we verify the effectiveness of the cluster-robust bandwidth selection and show that the derived cluster-robust confidence interval improves the coverage ratio. We illustrate the application of these methods using a policy-targeting dataset in development economics.

Explore related subjects

econ.EM stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Yuya Shimizu. 2024-12-28. Nonparametric Regression under Cluster Sampling. https://arxiv.org/abs/2403.04766

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Evidence Aggregation for Treatment Choice

Consider a planner who has limited knowledge of the policy's causal impact on a certain local population of interest due to a lack of data, but does have access to the publicized intervention studies performed for similar policies on different populations. How should the planner make use of and aggregate this existing evidence to make her policy decision? Following Manski (2020; Towards Credible Patient-Centered Meta-Analysis, \textit{Epidemiology}), we formulate the planner's problem as a statistical decision problem with a social welfare objective, and solve for an optimal aggregation rule under the minimax-regret criterion. We investigate the analytical properties, computational feasibility, and welfare regret performance of this rule. We apply the minimax regret decision rule to decide whether to enact an active labor market policy based on 14 randomized control trial studies.

econ.EM↗

arXiv2026

Beta-Sorted Portfolios

Beta-sorted portfolios---portfolios comprised of assets with similar covariation with selected risk factors---are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little is known of their econometric properties in contrast to comparable procedures such as two-pass regressions. We formally investigate the properties of beta-sorted portfolio returns by casting the procedure as a two-step nonparametric estimator with a nonparametric first step and a beta-adaptive portfolio construction. Our framework rationalizes the well-known estimation algorithm with precise economic and statistical assumptions on the general data-generating process. We provide conditions which ensure valid estimation and inference allowing for a range of hypotheses of interest in financial applications. We show that the rate of convergence of the estimator changes depending on the value of beta. We demonstrate that valid inference depends critically on the object of interest and discuss drawbacks of the widely used Fama-MacBeth variance estimator. To address these limitations, we propose a new variance estimator. We demonstrate the usefulness of our theoretical results in two empirical applications, including one in which we introduce a novel risk factor that captures the business credit cycle and show that it predicts both the cross-sectional and time-series behavior of U.S. stock returns.

econ.EM↗

arXiv2026

Difference-in-Differences with Unpoolable Data

Difference-in-differences (DID) is commonly used to estimate treatment effects but is infeasible in settings where data are unpoolable due to privacy concerns or legal restrictions on data sharing, particularly across jurisdictions. In this study, we identify and relax the assumption of data poolability in DID estimation. We propose an innovative approach to estimate DID with unpoolable data (UN-DID) which can accommodate covariates, multiple groups, and staggered adoption. Through analytical proofs and Monte Carlo simulations, we show that UN-DID and conventional DID estimates of the average treatment effect and standard errors are equal and unbiased in settings without covariates. With covariates, both methods produce estimates that are unbiased, equivalent, and converge to the true value. The estimates differ slightly but the statistical inference and substantive conclusions remain the same. Two empirical examples with real-world data further underscore UN-DID's utility. The UN-DID method allows the estimation of cross-jurisdictional treatment effects with unpoolable data, enabling better counterfactuals to be used and new research questions to be answered.

econ.EM↗