Description Usage Arguments Details Value Author(s) References See Also Examples
The (S3) generic function h.mcv
computes the modified
cross-validation bandwidth selector of r'th derivative of
kernel density estimator one-dimensional.
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x |
vector of data values. |
deriv.order |
derivative order (scalar). |
lower, upper |
range over which to minimize. The default is
almost always satisfactory. |
tol |
the convergence tolerance for |
kernel |
a character string giving the smoothing kernel to be used, with default
|
... |
further arguments for (non-default) methods. |
h.mcv
modified cross-validation implements for choosing the bandwidth h
of a r'th derivative kernel density estimator.
Stute (1992) proposed a so-called modified cross-validation (MCV) in kernel density estimator. This method can be extended to the estimation of derivative of a density, the essential idea based on approximated the problematic term by the aid of the Hajek projection (see Stute 1992). The minimization criterion is defined by:
MCV(h;r) = R(K(x;r))/ n h^(2r+1) + (-1)^r / n (n-1) h^(2r+1) sum( sum(varphi(x(j)-x(i)/h;r) ),i=1...n,j=1...n,j != i)
whit
varphi(c;r)= K(c;r)*K(c;r) - K(c;2r) - 0.5 mu(K(c)) K(c;2r+2)
and K(x;r)*K(x;r) is the convolution of the r'th derivative kernel function K(x;r)
(see kernel.conv
and kernel.fun
); R(K(x;r)) = int K(x;r)^2 dx and mu(K(x)) = int x^2 K(x) dx.
The range over which to minimize is hos
Oversmoothing bandwidth, the default is almost always
satisfactory. See George and Scott (1985), George (1990), Scott (1992, pp 165), Wand and Jones (1995, pp 61).
x |
data points - same as input. |
data.name |
the deparsed name of the |
n |
the sample size after elimination of missing values. |
kernel |
name of kernel to use |
deriv.order |
the derivative order to use. |
h |
value of bandwidth parameter. |
min.mcv |
the minimal MCV value. |
Arsalane Chouaib Guidoum acguidoum@usthb.dz
Heidenreich, N. B., Schindler, A. and Sperlich, S. (2013). Bandwidth selection for kernel density estimation: a review of fully automatic selectors. Advances in Statistical Analysis.
Stute, W. (1992). Modified cross validation in density estimation. Journal of Statistical Planning and Inference, 30, 293–305.
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