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 software package implementing our main results is provided.
Funding Statement
Cattaneo gratefully acknowledges financial support from the National Science Foundation through grants SES-1947805 and DMS-2210561, and from the National Institute of Health (R01 GM072611-16).
Jansson gratefully acknowledges financial support from the National Science Foundation through grant SES-1947662 and the research support of CREATES.
Acknowledgments
The authors thank the editor, two anonymous reviewers, Jianqing Fan, Jason Klusowski, Will Underwood, Jingshen Wang, and Rae Yu for their thoughtful discussions and valuable feedback.
Citation
Matias D. Cattaneo. Rajita Chandak. Michael Jansson. Xinwei Ma. "Boundary adaptive local polynomial conditional density estimators." Bernoulli 30 (4) 3193 - 3223, November 2024. https://doi.org/10.3150/23-BEJ1711
Information