OSCV (version 1.0)

h_OSCV_reg: The OSCV bandwidth in the regression context.

Description

Computing the OSCV bandwidth for the Gaussian local linear regression estimator. The Gaussian kernel is used in the bandwidth selection stage. The smoothness of the regression function is to be specified by the user.

Usage

h_OSCV_reg(desx, y, stype)

Arguments

desx

numerical vecror of design points,

y

numerical vecror of data points corresponding to the design points \(desx\),

stype

smoothness of the regression function: (\(stype=0\)) smooth function; (\(stype=1\)) nonsmooth function.

Value

The OSCV bandwidth (scalar).

Details

Computing the OSCV bandwidth for the data vector \((desx,y)\). The Gaussian kernel is used for the cross-validation purposes and in the stage of computing the resulting local linear regression estimate. No additional rescaling of the computed bandwidth is needed. The smoothness of the regression function \(stype\), essentially, determines the value of the bandwidth rescaling constant that is chosen in the body of the function. Thus, the constant is equal to 0.6168471 in the smooth case, and 0.5730 in the nonsmooth case. See Savchuk, Hart and Sheather (2016). The OSCV bandwidth is the minimizer of the OSCV function OSCV_reg.

References

• Hart, J.D. and Yi, S. (1998). One-sided cross-validation. Journal of the American Statistical Association, 93(442), 620-631.
• Savchuk, O.Y., Hart, J.D., Sheather, S.J. (2013). One-sided cross-validation for nonsmooth regression functions. Journal of Nonparametric Statistics, 25(4), 889-904.
• Savchuk, O.Y., Hart, J.D., Sheather, S.J. (2016). Corrigendum to "One-sided cross-validation for nonsmooth regression functions". Journal of Nonparametric Statistics, 28(4), 875-877.
• 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.

See Also

OSCV_reg, loclin, C_smooth, h_OSCV_dens, h_ASE_reg.

Examples

## Not run: ------------------------------------
# # Example (Old Faithful geyser)
# xdat=faithful[[2]]     # waiting time
# ydat=faithful[[1]]     # eruption duration
# u=seq(40,100,len=1000)
# h_oscv=round(h_OSCV_reg(xdat,ydat,0),digits=4)
# l=loclin(u,xdat,ydat,h_oscv)
# dev.new()
# plot(xdat,ydat,pch=20,cex=1.5,cex.axis=1.7,cex.lab=1.7,xlab="waiting time",
# ylab="eruption duration")
# lines(u,l,'l',lwd=3)
# title(main="Data and LLE",cex.main=1.7)
# legend(35,5,legend=paste("h_OSCV=",h_oscv),cex=2,bty="n")
# legend(80,3,legend="n=272",cex=2,bty="n")
## ---------------------------------------------