Dear everyone,
I'm coding the Horowitz-Spokoiny (2001) test [1], and I would be very
grateful or some advice regarding the Kernel density (apologies
beforehand if my terminology is not fully correct). I have looked into
ksmooth and npreg, but with no success.
Given a (n x p) matrix of covariates X, I need to construct the
following matrix of Kernel densities or weights:
w(x_i, x_j) =
K(x_i - x_j)
-----------------------------
sum_{k=1}^n K(x_i - x_k)
where x_i, x_j, x_k are (1 x p) vectors, and K is a multivariate normal
kernel. The resulting weighting matrix W has dimension (n x n).
I have looked into npreg, but if I get this correctly, it does not
output this weighting matrix. I do need the weighting matrix itself
for the test statistic, and not just the kernel regression
estimates. I can construct it myself, but I thought I'd ask around
before doing so.
Best,
Stephan
[1] Horowitz Joel L. and Spokoiny Vladimir G. (2001): "An Adaptive,
Rate-Optimal Test of a Parametric Mean-Regression Model against a
Nonparametric Alternative". Econometrica, Vol. 69, No. 3 (May, 2001),
pp. 599-631
--
-----------------------
Stephan Lindner
University of Michigan
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