Abstract
Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, survival analysis, propensity score and panel data models. We develop the limit theory for a kernel-weighted specification test of a parametric conditional mean when the law of the regressors may not be absolutely continuous to the Lebesgue measure and admits non-trivial singular components. In the special case of absolutely continuous measures, our approach weakens the usual regularity conditions. This result is of independent interest and may be useful in other applications that utilize kernel smoothed statistics. Simulations illustrate the non-trivial impact of the distribution of the conditioning variables on the power properties of the test statistic.
Funding Statement
Sid Kankanala gratefully acknowledges financial support from the Cowles Foundation for Research in Economics. Victoria Zinde-Walsh gratefully acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), [Reference grant 253139].
Acknowledgments
The authors are grateful to Donald Andrews, Xiaohong Chen, Yuichi Kitamura, Renaud Raquépas, Michael R Sullivan and Edward Vytlacil for their suggestions and constructive comments. The authors also thank the anonymous referees and associate editor for valuable criticism and remarks that improved the quality of this paper.
Citation
Sid Kankanala. Victoria Zinde-Walsh. "Kernel-weighted specification testing under general distributions." Bernoulli 30 (3) 1921 - 1944, August 2024. https://doi.org/10.3150/23-BEJ1658
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