TY - JOUR
T1 - Local regression distribution estimators
AU - Cattaneo, Matias D.
AU - Jansson, Michael
AU - Ma, Xinwei
N1 - Funding Information:
Prepared for “Celebrating Whitney Newey’s Contributions to Econometrics” Conference at MIT, May 17–18, 2019. We thank the conference participants for comments, and Guido Imbens and Yingjie Feng for very useful discussions. We are also thankful to the handling co-Editor, Xiaohong Chen, an Associate Editor and two reviewers for their input. Cattaneo gratefully acknowledges financial support from the National Science Foundation, United States of America through grant SES-1947805 , and Jansson gratefully acknowledges financial support from the National Science Foundation, United States of America through grant SES-1947662 and the research support of CREATES, Denmark .
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021
Y1 - 2021
N2 - This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample distributional approximation in a unified way, allowing for both boundary and interior evaluation points simultaneously. Using this result, we study the asymptotic efficiency of the estimators, and show that a carefully crafted minimum distance implementation based on “redundant” regressors can lead to efficiency gains. Second, we establish uniform linearizations and strong approximations for the estimators, and employ these results to construct valid confidence bands. Third, we develop extensions to weighted distributions with estimated weights and to local L2 estimation. Finally, we illustrate our methods with two applications in program evaluation: counterfactual density testing, and IV specification and heterogeneity density analysis. Companion software packages in Stata and R are available.
AB - This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample distributional approximation in a unified way, allowing for both boundary and interior evaluation points simultaneously. Using this result, we study the asymptotic efficiency of the estimators, and show that a carefully crafted minimum distance implementation based on “redundant” regressors can lead to efficiency gains. Second, we establish uniform linearizations and strong approximations for the estimators, and employ these results to construct valid confidence bands. Third, we develop extensions to weighted distributions with estimated weights and to local L2 estimation. Finally, we illustrate our methods with two applications in program evaluation: counterfactual density testing, and IV specification and heterogeneity density analysis. Companion software packages in Stata and R are available.
KW - Distribution and density estimation
KW - Efficiency
KW - Local polynomial methods
KW - Optimal kernel
KW - Program evaluation
KW - Uniform approximation
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U2 - 10.1016/j.jeconom.2021.01.006
DO - 10.1016/j.jeconom.2021.01.006
M3 - Article
AN - SCOPUS:85102022450
SN - 0304-4076
JO - Journal of Econometrics
JF - Journal of Econometrics
ER -