Nonparametric estimation and testing on discontinuity of positive supported densities: A kernel truncation approach
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Date
2016
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Abstract
Discontinuity in density functions is of economic importance and interest.
For instance, in studies on regression discontinuity designs, discontinuity in
the density of a running variable suggests violation of the no-manipulation
assumption. In this paper we develop estimation and testing procedures on
discontinuity in densities with positive support. Our approach is built on splitting
the gamma kernel (Chen, 2000) into two parts at a given (dis)continuity
point and constructing two truncated kernels. The jump-size magnitude of the
density at the point can be estimated nonparametrically by two kernels and a
multiplicative bias correction method. The estimator is easy to implement, and
its convergence properties are delivered by various approximation techniques on
incomplete gamma functions. Based on the jump-size estimator, two versions
of test statistics for the null of continuity at a given point are also proposed.
Moreover, estimation theory of the entire density in the presence of a discontinuity
point is explored. Monte Carlo simulations confirm nice finite-sample
properties of the jump-size estimator and the test statistics.
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Keywords
boundary bias, regression discontinuity design, nonparametric kernel testing, incomplete gamma functions, gamma kernel, discontinuous probability density, density estimation