A nonparametric discontinuity test of density using a beta kernel

Gaku Igarashi

Journal of Nonparametric Statistics, 2023, vol. 35, issue 2, 323-354

Abstract: In regression discontinuity design (RDD), the continuity of the density of a running variable is required. Hence, a discontinuity test of density is used for RDD. In previous studies, tests using difference estimators between the left- and right-hand limits of a density at a (potential) discontinuity point were suggested. In the present paper, a new discontinuity test based on direct density ratio estimation using a beta kernel is proposed. By using the ratio estimator in the proposed test statistic, rather than a difference estimator, the characteristic form of the asymptotic variance of the test statistic is obtained. Consequently, the power of the proposed test is shown to increase when used as a one-tailed test. Simulation studies illustrate the larger power of the proposed test when used as a one-tailed test.

Date: 2023
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DOI: 10.1080/10485252.2022.2150766

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