Abstract
This paper improves a kernel-smoothed test of symmetry through combining it with a new class of asymmetric kernels called the generalized gamma kernels. It is demonstrated that the improved test statistic has a normal limit under the null of symmetry and is consistent under the alternative. A test-oriented smoothing parameter selection method is also proposed to implement the test. Monte Carlo simulations indicate superior finite-sample performance of the test statistic. It is worth emphasizing that the performance is grounded on the first-order normal limit and a small number of observations, despite a nonparametric convergence rate and a sample-splitting procedure of the test.
Highlights
Symmetry and conditional symmetry play a key role in numerous fields of economics and finance
The SSST developed by FMS is built on the idea of gauging the closeness between right and left sides of the axis of symmetry of an unknown pdf
The test statistic can be interpreted as a standardized version of a degenerate U-statistic
Summary
Symmetry and conditional symmetry play a key role in numerous fields of economics and finance. The split-sample approach is expected to result in efficiency loss It can attain the same convergence rate as the smoothed symmetry tests using symmetric kernels do. While existing articles on asymmetric kernel-smoothed tests (e.g., Fernandes and Grammig [33]; FMS) borrow the choice method based on optimality for density estimation, we tailor the idea of test-oriented smoothing parameter selection by Kulasekera and Wang [34,35] to the SSST. The superior performance is based on first-order asymptotic results, and the assistance of bootstrapping appears to be unnecessary, unlike most of the smoothed tests employing fixed, symmetric kernels. In order to describe different asymptotic properties of an asymmetric kernel estimator across positions of the design point x (> 0) relative to the smoothing parameter b (> 0) that shrinks toward zero, we denote by “interior x” and “boundary x” a design point x that satisfies x/b → ∞ and x/b → κ for some 0 < κ < ∞ as b → 0, respectively
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
