Nadaraya-Watson kernel regression (alias of hrzk2)

This module is an ALIAS. The estimator is implemented once, in hrzk2; this entry point supplies the classical argument spelling (bandwidth h) and delegates.

Usage

Naday(x, y, h = NULL, grid = NULL)

Arguments

x: Numeric covariate vector.
y: Numeric response vector.
h: Optional bandwidth (Silverman default).
grid: Optional evaluation grid (defaults to x).

Value

List with estimate, se, bandwidth, n, method.

Details

m_hat(x) = sum_i K_h(x - X_i) Y_i / sum_i K_h(x - X_i) with a Gaussian kernel and, when h is omitted, Silverman's rule-of-thumb bandwidth.

References

Nadaraya (1964), Theory Probab. Appl. 9(1), 141-142, doi:10.1137/1109020 ; Watson (1964), Sankhya A 26(4), 359-372.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Naday(V, V)
#> $estimate
#> [1] 2.076520 2.574346 3.245343 4.062417 4.937583 5.754657 6.425654 6.923480
#> 
#> $se
#> [1] 0.5710726 0.5891685 0.6258682 0.6540584 0.6540584 0.6258682 0.5891685
#> [8] 0.5710726
#> 
#> $bandwidth
#> [1] 1.713024
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Nadaraya-Watson kernel regression (Gaussian)"
#>