| Title: | Bandwidth Selector with Penalized Comparison to Overfitting Criterion |
|---|---|
| Description: | Bandwidth selector according to the Penalised Comparison to Overfitting (P.C.O.) criterion as described in Varet, S., Lacour, C., Massart, P., Rivoirard, V., (2019) <https://hal.archives-ouvertes.fr/hal-02002275>. It can be used with univariate and multivariate data. |
| Authors: | S. Varet |
| Maintainer: | S. Varet <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.0.1 |
| Built: | 2024-12-07 06:51:24 UTC |
| Source: | CRAN |
Bandwidth selector according to the Penalised Comparison to Overfitting (P.C.O.) criterion as described in Varet, S., Lacour, C., Massart, P., Rivoirard, V., (2019). It can be used with univariate and multivariate data.
bw.L2PCO(x_i, ...)
bw.L2PCO.diag(x_i, ...)
select the optimal bandwith according to PCO criterion where x_i are the data (a numeric matrix or a numeric vector).
S. Varet.
Maintainer: S. Varet <[email protected]>
Varet, S., Lacour, C., Massart, P., Rivoirard, V., (2019). Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation. hal-02002275. https://hal.archives-ouvertes.fr/hal-02002275
# load univariate data data("gauss_1D_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value bw.L2PCO(gauss_1D_sample)# load univariate data data("gauss_1D_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value bw.L2PCO(gauss_1D_sample)
bw.L2PCO tries to minimise the PCO criterion (described and studied in Varet, S., Lacour, C., Massart, P.,
Rivoirard, V., (2019)) with a gold section search. For multivariate data,
it searches for a full matrix.
bw.L2PCO( x_i, nh = 40, K_name = "gaussian", binning = FALSE, nb = 32, tol = 1e-06, adapt_nb_bin = FALSE, nb_bin_vect = NULL )bw.L2PCO( x_i, nh = 40, K_name = "gaussian", binning = FALSE, nb = 32, tol = 1e-06, adapt_nb_bin = FALSE, nb_bin_vect = NULL )
x_i |
the observations. Must be a matrix with d column and n lines (d the dimension and n the sample size) |
nh |
the maximum number of PCO criterion evaluations during the golden section search. The default value is 40. The golden section search stop once this value is reached or if the tolerance is achieved, and return the middle of the interval. |
K_name |
name of the kernel. Can be 'gaussian', 'epanechnikov', or 'biweight'. The default value is 'gaussian'. |
binning |
default value is FALSE, that is the function computes the exact PCO criterion. If set to TRUE allows to use binning. |
nb |
is the number of bins to use when binning is TRUE. For multivariate x_i, nb corresponds to the number of bins per dimension. The default value is 32. |
tol |
is the maximum authorized length of the interval which contains the optimal h for univariate data. For multivariate data, it corresponds to the length of each hypercube axe. The golden section search stop once this value is achieved or when nh is reached and return the middle of the interval. Its default value is 10^(-6). |
adapt_nb_bin |
is a boolean used for univariate x_i. If set to TRUE, authorises the function to increase the number of bins if, with nb bins, the middle of the initial interval is not an admissible solution, that is if the criterion at the middle is greater than the mean of the criterion at the bounds of the initial interval of search. |
nb_bin_vect |
can be set to have a different number of bins on each dimension |
a scalar for univariate data or a matrix for multivariate data corresponding to the optimal bandwidth according to the PCO criterion
Varet, S., Lacour, C., Massart, P., Rivoirard, V., (2019). Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation. hal-02002275. https://hal.archives-ouvertes.fr/hal-02002275
[stats::nrd0()], [stats::nrd()], [stats::ucv()], [stats::bcv()] and [stats::SJ()] for other univariate bandwidth selection and [stats::density()] to compute the associated density estimation.
[ks::Hlscv()], [ks::Hbcv()], [ks::ns()] for other multivariate bandwidth selection.
# an example with simulated univariate data # load univariate data data("gauss_1D_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value bw.L2PCO(gauss_1D_sample) # an example with simulated multivariate data # load multivariate data data("gauss_mD_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value # generates a warning since the tolerance value is not reached bw.L2PCO(gauss_mD_sample) # To avoid this warning, it is possible to increase the parameter nh bw.L2PCO(gauss_mD_sample, nh = 80)# an example with simulated univariate data # load univariate data data("gauss_1D_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value bw.L2PCO(gauss_1D_sample) # an example with simulated multivariate data # load multivariate data data("gauss_mD_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value # generates a warning since the tolerance value is not reached bw.L2PCO(gauss_mD_sample) # To avoid this warning, it is possible to increase the parameter nh bw.L2PCO(gauss_mD_sample, nh = 80)
bw.L2PCO.diag tries to minimise the PCO criterion (described and studied in Varet, S., Lacour, C.,
Massart, P., Rivoirard, V., (2019)) with a gold section search. For multivariate data,
it searches for a diagonal matrix.
bw.L2PCO.diag( x_i, nh = 40, K_name = "gaussian", binning = FALSE, nb = 32, tol = 1e-06, adapt_nb_bin = FALSE, nb_bin_vect = NULL )bw.L2PCO.diag( x_i, nh = 40, K_name = "gaussian", binning = FALSE, nb = 32, tol = 1e-06, adapt_nb_bin = FALSE, nb_bin_vect = NULL )
x_i |
the observations. Must be a matrix with d column and n lines (d the dimension and n the sample size) |
nh |
the maximum of possible bandwiths tested. The default value is 40. |
K_name |
name of the kernel. Can be 'gaussian', 'epanechnikov', or 'biweight'. The default value is 'gaussian'. |
binning |
can be set to TRUE or FALSE. The value TRUE allows to use binning. The default value FALSE computes the exact PCO criterion. |
nb |
is the number of bins to use when binning is TRUE. For multivariate x_i, nb corresponds to the number of bins per dimension. |
tol |
is the maximum authorized length of the interval which contains the optimal h for univariate data. For multivariate data, it corresponds to the length of each hypercube axe. The golden section search stop once this value is achieved or when nh is reached and return the middle of the interval. Its default value is 10^(-6). |
adapt_nb_bin |
is a boolean used for univariate x_i. If set to TRUE, authorises the function to increase the number of bins if, with nb bins, the middle of the initial interval is not an admissible solution, that is if the criterion at the middle is greater than the mean of the criterion at the bounds of the initial interval of search. |
nb_bin_vect |
can be set to have a different number of bins on each dimension |
a scalar for univariate data or a vector (the diagonal of the matrix) for multivariate data corresponding to the optimal bandwidth according to the PCO criterion
Varet, S., Lacour, C., Massart, P., Rivoirard, V., (2019). Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation. hal-02002275. https://hal.archives-ouvertes.fr/hal-02002275
[stats::nrd0()], [stats::nrd()], [stats::ucv()], [stats::bcv()] and [stats::SJ()] for other univariate bandwidth selection and [stats::density()] to compute the associated density estimation.
[ks::Hlscv.diag()], [ks::Hbcv.diag()], [ks::ns.diag()] for other multivariate bandwidth selection.
# an example with simulated univariate data # load univariate data data("gauss_1D_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value bw.L2PCO.diag(gauss_1D_sample) # an example with simulated multivariate data # load multivariate data data("gauss_mD_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value # generates a warning since the tolerance value is not reached bw.L2PCO.diag(gauss_mD_sample) # To avoid this warning, it is possible to increase the parameter nh bw.L2PCO.diag(gauss_mD_sample, nh = 80)# an example with simulated univariate data # load univariate data data("gauss_1D_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value bw.L2PCO.diag(gauss_1D_sample) # an example with simulated multivariate data # load multivariate data data("gauss_mD_sample") # computes the optimal bandwith for the sample x_i with all parameters set to their default value # generates a warning since the tolerance value is not reached bw.L2PCO.diag(gauss_mD_sample) # To avoid this warning, it is possible to increase the parameter nh bw.L2PCO.diag(gauss_mD_sample, nh = 80)
A univariate sample of 100 realisations of a gaussian law with mean 0 and standard deviation 1
data("gauss_1D_sample")data("gauss_1D_sample")
A vector with 100 rows
A 2D sample of 100 realisations of a gaussian law with mean (0, 0) and covariance matrix | 1 0.9 | | 0.9 1 |
data("gauss_mD_sample")data("gauss_mD_sample")
A matrix with 100 rows and 2 columns