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Boundary Adaptive Local Polynomial Conditional Density Estimators

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  • Matias D. Cattaneo
  • Rajita Chandak
  • Michael Jansson
  • Xinwei Ma

Abstract

We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the estimators, offering characterizations of both probability concentration and distributional approximation. In particular, we establish uniform convergence rates in probability and valid Gaussian distributional approximations for the Studentized t-statistic process. We also discuss implementation issues such as consistent estimation of the covariance function for the Gaussian approximation, optimal integrated mean squared error bandwidth selection, and valid robust bias-corrected inference. We illustrate the applicability of our results by constructing valid confidence bands and hypothesis tests for both parametric specification and shape constraints, explicitly characterizing their approximation errors. A companion R software package implementing our main results is provided.

Suggested Citation

  • Matias D. Cattaneo & Rajita Chandak & Michael Jansson & Xinwei Ma, 2022. "Boundary Adaptive Local Polynomial Conditional Density Estimators," Papers 2204.10359, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2204.10359
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Yuta Koike, 2019. "Improved Central Limit Theorem and bootstrap approximations in high dimensions," Papers 1912.10529, arXiv.org, revised May 2022.
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