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Nonparametric Regression under Cluster Sampling

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  • Yuya Shimizu

    (Department of Economics, University of Wisconsin, Madison, U.S.A. and Junior Research Fellow, Research Institute for Economics & Business Administration (RIEB), Kobe University, JAPAN)

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.

Suggested Citation

  • Yuya Shimizu, 2024. "Nonparametric Regression under Cluster Sampling," Discussion Paper Series DP2024-20, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2024-20
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2024-20.pdf
    File Function: First version, 2024
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