vardif {VarED}

Estimate Residual Variance with Differene-Based Method.

Description

Estimate residual variance with differene-based method.

Usage

vardif(x, y, type, r, m)

Arguments

x

numeric Equally spaced design points.

y

numeric Responses

type

character Taking "opt" or "ord", default as "ord"

r

numeric The order of employed difference sequence.

m

numeric The bandwidth or the number of regressors.

Value

u

numeric The estimated variance.

References

Tong, T. and Wang, Y. (2005). Estimating residual variance in nonparametric regression using least squares, Biometrika 92: 821 - 830.

Wenlin Dai, Tiejun Tong and Lixing Zhu (2017) Optimal sequence or ordinary sequence? A unified framework for variance estimation in nonparametric regression, Statistical Science.

Examples

x<-1:100/100
y<-5*sin(2*pi*x)+rnorm(100)*0.5
type="ord"
r<-2
m<-10
vardif(x,y,type,r,m)