Description Usage Arguments Details Value References See Also Examples
Function, vectorized in its first argument sigma
, to compute the
“updated” weights W_{ni} in eq. (2.1) of Eichner & Stute (2012) for
the kernel adjusted regression estimator.
1  weights_ES2012(sigma, xXh, thetaXh, K, h)

sigma 
Numeric vector (σ_1, …, σ_s) with s ≥ 1 with values of the scale parameter σ. 
xXh 
Numeric vector expecting the precomputed hscaled differences (x  X_1)/h, ..., (x  X_n)/h where x is the single (!) location for which the weights are to be computed, the X_i's are the data values, and h is the numeric bandwidth scalar. 
thetaXh 
Numeric vector expecting the precomputed hscaled differences
(θ  X_1)/h, ..., (θ  X_n)/h where
θ is the numeric scalar location parameter, and the
X_i's and h are as in 
K 
A kernel function (with vectorized in & output) to be used for the estimator. 
h 
Numeric scalar for bandwidth h (as “contained” in

Note that it is not immediately obvious that W_{ni} in eq. (2.1) of
Eichner & Stute (2012) is a function of σ. In fact, W_{ni}
= W_{ni}(x; h, θ, σ) as can be seen on p. 2542 ibid. The
computational version implemented here, however, is given in (15.19) of
Eichner (2017). Precomputed (x  X_i)/h and (θ  X_i)/h,
i = 1, …, n are expected for efficiency reasons (and are
currently prepared in function kare
).
If length(sigma)
> 1 a numeric matrix of the dimension
length(sigma)
by length(xXh)
with elements
(W_{ni}(x; h, θ, σ_r)) for r = 1, …,
length(sigma)
and i = 1, …, length(xXh)
;
otherwise a numeric vector of the same length as xXh
.
Eichner & Stute (2012) and Eichner (2017): see kader
.
bias_ES2012
and var_ES2012
which both
call this function, and kare
which currently does
the precomputing.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  require(stats)
# Regression function:
m < function(x, x1 = 0, x2 = 8, a = 0.01, b = 0) {
a * (x  x1) * (x  x2)^3 + b
}
# Note: For a few details on m() see examples in ?nadwat.
n < 100 # Sample size.
set.seed(42) # To guarantee reproducibility.
X < runif(n, min = 3, max = 15) # X_1, ..., X_n # Design.
Y < m(X) + rnorm(length(X), sd = 5) # Y_1, ..., Y_n # Response.
h < n^(1/5)
Sigma < seq(0.01, 10, length = 51) # sigmagrid for minimization.
x0 < 5 # Location at which the estimator of m should be computed.
# Weights (W_{ni}(x; \sigma_r))_{1<=r<=length(Sigma), 1<=i<=n} for
# Var_n(sigma) and Bias_n(sigma) each at x0 on the sigmagrid:
weights_ES2012(sigma = Sigma, xXh = (x0  X) / h,
thetaXh = (mean(X)  X) / h, K = dnorm, h = h)

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