h.mlcv {kedd} | R Documentation |
Maximum-Likelihood Cross-validation for Bandwidth Selection
Description
The (S3) generic function h.mlcv
computes the maximum
likelihood cross-validation (Kullback-Leibler information)
bandwidth selector of a one-dimensional kernel density estimate.
Usage
h.mlcv(x, ...)
## Default S3 method:
h.mlcv(x, lower = 0.1, upper = 5, tol = 0.1 * lower,
kernel = c("gaussian", "epanechnikov", "uniform", "triangular",
"triweight", "tricube", "biweight", "cosine"), ...)
Arguments
x |
vector of data values. |
lower , upper |
range over which to maximize. 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. |
Details
h.mlcv
maximum-likelihood cross-validation implements for choosing
the optimal bandwidth h
of kernel density estimator.
This method was proposed by Habbema, Hermans, and Van den Broeck (1971) and by Duin (1976). The maximum-likelihood cross-validation (MLCV) function is defined by:
MLCV(h) = n^{-1} \sum_{i=1}^{n} \log\left[\hat{f}_{h,i}(x)\right]
the estimate \hat{f}_{h,i}(x)
on the subset \{X_{j}\}_{j \neq i}
denoting the leave-one-out estimator, can be written:
\hat{f}_{h,i}(X_{i}) = \frac{1}{(n-1) h} \sum_{j \neq i} K \left(\frac{X_{j}-X_{i}}{h}\right)
Define that h_{mlcv}
as good which approaches the finite maximum of MLCV(h)
:
h_{mlcv} = \arg \max_{h} MLCV(h) = \arg \max_{h} \left(n^{-1} \sum_{i=1}^{n} \log\left[\sum_{j \neq i} K \left(\frac{X_{j}-X_{i}}{h}\right)\right]-\log[(n-1)h]\right)
Value
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 |
h |
value of bandwidth parameter. |
mlcv |
the maximal likelihood CV value. |
Author(s)
Arsalane Chouaib Guidoum acguidoum@usthb.dz
References
Habbema, J. D. F., Hermans, J., and Van den Broek, K. (1974) A stepwise discrimination analysis program using density estimation. Compstat 1974: Proceedings in Computational Statistics. Physica Verlag, Vienna.
Duin, R. P. W. (1976). On the choice of smoothing parameters of Parzen estimators of probability density functions. IEEE Transactions on Computers, C-25, 1175–1179.
See Also
plot.h.mlcv
, see lcv
in package locfit.
Examples
h.mlcv(bimodal)
h.mlcv(bimodal, kernel ="epanechnikov")