# CV_reg: The cross-validation (CV) function in the regression context. In OSCV: One-Sided Cross-Validation

## Description

Computing CV(h), the value of the CV function in the regression context.

## Usage

 `1` ```CV_reg(h, desx, y) ```

## Arguments

 `h` numerical vector of bandwidth values, `desx` numerical vecror of design points, `y` numerical vecror of data values corresponding to the design points desx.

## Details

The CV function is a measure of fit of the regression estimate to the data. The local linear estimator based on the Gaussian kernel is used. The cross-validation bandwidth is the minimizer of the CV function.

## Value

The vector of values of CV(h) for the correponsing vector of h values.

## References

Stone, C.J. (1977) Consistent nonparametric regression. Annals of Statistics, 5(4), 595-645.

`loclin`, `h_ASE_reg`, `ASE_reg`, `OSCV_reg`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## Not run: # Example (Old Faithful geyser). Take x=waiting time; y=eruption duration. The sample size n=272. xdat=faithful[[2]] ydat=faithful[[1]] harray=seq(0.5,10,len=100) cv=CV_reg(harray,xdat,ydat) R=range(xdat) h_cv=round(optimize(CV_reg,c(0.01,(R[2]-R[1]/4)),desx=xdat,y=ydat)\$minimum,digits=4) dev.new() plot(harray,cv,'l',lwd=3,xlab="h",ylab="CV(h)",main="CV function for the Old Faithful geyser data", cex.lab=1.7,cex.axis=1.7,cex.main=1.5) legend(6,0.155,legend="n=272",cex=1.8,bty="n") legend(1,0.18,legend=paste("h_CV=",h_cv),cex=2,bty="n") ## End(Not run) ```