bw_select_cv_univariate {lg} | R Documentation |
Cross-validation for univariate distributions
Description
Uses cross-validation to find the optimal bandwidth for a univariate locally Gaussian fit
Usage
bw_select_cv_univariate(x, tol = 10^(-3))
Arguments
x |
The vector of data points. |
tol |
The absolute tolerance in the optimization, passed to the
|
Details
This function provides the univariate version of the Cross Validation
algorithm for bandwidth selection described in Otneim & Tjøstheim (2017),
Section 4. Let \hat{f}_h(x)
be the univariate locally Gaussian density
estimate obtained using the bandwidth h
, then this function returns the
bandwidth that maximizes
CV(h) = n^{-1} \sum_{i=1}^n \log
\hat{f}_h^{(-i)}(x_i),
where \hat{f}_h^{(-i)}
is the density estimate
calculated without observation x_i
.
Value
The function returns a list with two elements: bw
is the
selected bandwidth, and convergence
is the convergence flag returned
by the optim
-function.
References
Otneim, Håkon, and Dag Tjøstheim. "The locally gaussian density estimator for multivariate data." Statistics and Computing 27, no. 6 (2017): 1595-1616.
Examples
x <- rnorm(100)
bw <- bw_select_cv_univariate(x)