Bandwidth Selection in Nonparametric Kernel Testing

By Jiti Gao, Irène Gijbels. 2008

154 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3764a8a791d0ecfa58f015790ccfb9eb276ad216

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Citations in the corpus

NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY (2009, unknown): “3 of Gao and Gijbels, 2008) suggest using an approximate version of the form ĥtest = â−1/2Ĉ−3/2T , (3.5) where Ĉ2T = ∑ T t=1 ̂2(Xt ,θ̂1) p̂(Xt ) μ̂2 √ 2ν̂2 ∫ K 2(v)dv and â = √ 2K (3)(0) 3 (√∫ K 2(u)du )3 ĉ(p) with ĉ(p) = 1 T ∑ T t=1 p̂2(Xt )(√ 1 T ∑ T t=1 p̂(Xt ) )3 , in which μ̂2 = 1T…”
Testing functional inequalities (2011, methodology): “The methods of Gao and Gijbels (2008) are not directly applicable to our tests, and it is a challenging problem to develop a theory of optimal bandwidths for our tests.”
An updated review of Goodness-of-Fit tests for regression models (2013, background): “Although the literature is relatively scarce on this topic, it is worth citing the works by Kulasekera and Wang (1997), Zhang (2003, 2004) or more recently, Gao and Gijbels (2008).”
Specification testing in nonlinear and nonstationary time series autoregression (2009, background): “can be shown that E " XT t=1 XT s=1,s6= t a2 st(u 2 s −1) ! u2 t #2 =o(σ4 (A.51) T) using E[u2 1]=1. Let Q(u)= K 2(u) J02 . Then Q(·) is a probability kernel. Applying Lemma C.1 in Appendix C of Gao et al. (2008), we may show that as T→∞ 1 T XT t=1 1 N(T)h T s=1 Q Xs−1 −Xt−1 h !! u2 t = 1 T XT ”
Inference of time-varying regression models (2012, background): “Bandwidth selection for nonparametric hypothesis testing is a nontrivial problem, and it has been studied in [15, 21, 22, 30] among many others.”
HIGHER-ORDER ACCURATE, POSITIVE SEMIDEFINITE ESTIMATION OF LARGE-SAMPLE COVARIANCE AND SPECTRAL DENSITY MATRICES (2005, background): “Sun, Phillips, and Jin (2008) make this point eloquently, and devise a criterion to be optimized that is a weighted combination of type I and II errors, thus taking into account size and power at the same time; see also Gao and Gijbels (2008), and Sun and Phillips (2008) for related discussions.”