Description Usage Arguments Details Value References See Also Examples
The one-sided counterpart of the kernel H_I
. See expressions (15) and (8) of Savchuk and Hart (2017).
1 |
u |
numerical vector of argument values, |
alpha |
first parameter of the cross-validation kernel L_I, |
sigma |
second parameter of the cross-validation kernel L_I. |
The family of the one-sided cross-validation kernels L_I indexed by the parameters -∞<α<∞ and σ>0. This family is used in the OSCV implementations in both regression context (see Savchuk and Hart (2017)) and density estimation context (see Savchuk (2017)). The special members of the family:
The robust kernel used in Savchuk and Hart (2017) and Savchuk (2017) is obtained by setting α=16.8954588 and σ=1.01;
The one-sided Gaussian kernel L_G is obtained by either setting α=0 for any σ>0 or by setting σ=1 for any -∞<α<∞.
The bandwidth selected by L_I should be multiplied by a reascaling constant before it is used in computing the ultimate Gaussian (regression or density) estimate. In the case of a smooth (regression or density) function the rescaling constant is C_smooth
.
The value of L_I(u;α,σ).
Savchuk, O.Y., Hart, J.D. (2017). Fully robust one-sided cross-validation for regression functions. Computational Statistics, doi:10.1007/s00180-017-0713-7.
Savchuk, O.Y. (2017). One-sided cross-validation for nonsmooth density functions, arXiv:1703.05157.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ## Not run:
# Plotting the robust one-sided kernel from Savchuk and Hart (2017) with
# alpha=16.8954588 and sigma=1.01.
u=seq(-1,5,len=1000)
rker=L_I(u,16.8954588,1.01)
Gker=L_I(u,0,1)
dev.new()
plot(u,rker,'l',lwd=3,cex.axis=1.7, cex.lab=1.7)
title(main="One-sided kernels: L_I (robust) and L_G",cex=1.7)
lines(u,Gker,lty="dashed",lwd=3)
legend(0.5,2.5,lty=c("solid","dashed"),lwd=c(3,3),legend=c("L_I","L_G"),cex=1.7)
legend(2,1.5,legend=c("alpha=16.8955","sigma=1.01"),cex=1.5)
## End(Not run)
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