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 pre-computed h-scaled 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 pre-computed h-scaled 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). Pre-computed (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 pre-computing.
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) # sigma-grid 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 sigma-grid:
weights_ES2012(sigma = Sigma, xXh = (x0 - X) / h,
thetaXh = (mean(X) - X) / h, K = dnorm, h = h)
|
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