| Title: | Robust Likelihood Cross Validation Bandwidth Selection |
| Version: | 1.0.0 |
| Description: | Robust likelihood cross validation bandwidth for uni- and multi-variate kernel densities. It is robust against fat-tailed distributions and/or outliers. Based on "Robust Likelihood Cross-Validation for Kernel Density Estimation," Wu (2019) <doi:10.1080/07350015.2018.1424633>. |
| License: | GPL (≥ 3) |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.2 |
| Imports: | statmod, stats |
| Suggests: | rmarkdown, knitr, copula |
| VignetteBuilder: | knitr |
| URL: | https://sites.google.com/tamu.edu/ximingwu/ |
| NeedsCompilation: | no |
| Packaged: | 2022-03-03 02:45:29 UTC; wuxim |
| Author: | Ximing Wu [aut, cre] |
| Maintainer: | Ximing Wu <xwu@tamu.edu> |
| Repository: | CRAN |
| Date/Publication: | 2022-03-07 20:30:08 UTC |
Univariate kernel density
Description
Univariate kernel density
Usage
kde(x.obs, x.new = NULL, h)
Arguments
x.obs |
Training (observed) data (n1 vector) |
x.new |
Evaluation data (n2 vector); default to x.obs |
h |
Bandwidth |
Value
Density evaluated at x.new
Author(s)
Ximing Wu xwu@tamu.edu
References
Wu, Ximing (2019), "Robust Likelihood Cross Validation for Kernel Density Estimation," Journal of Business and Economic Statistics, 37(4): 761-770.
Examples
x=rnorm(100)
x.new=seq(-5,5,length=50)
h=1.06*sd(x)*(length(x))^(-1/5)
f=kde(x.new=x.new,x.obs=x,h=h)
Multivariate kernel density
Description
Multivariate kernel density
Usage
kde_d(x.obs, x.new = NULL, h, stud = FALSE)
Arguments
x.obs |
Training (observed) data (n1 by d matrix, d>=2) |
x.new |
Evaluation data (n2 by d matrix, d>=2); default to x.obs |
h |
Bandwidth (d vector) |
stud |
Indicator for whether data are studentized; default to FALSE |
Details
For multivariate distributions, bandwidth is calculated for studentized data.
Value
Density evaluated at x.new
Author(s)
Ximing Wu xwu@tamu.edu
References
Wu, Ximing (2019), "Robust Likelihood Cross Validation for Kernel Density Estimation," Journal of Business and Economic Statistics, 37(4): 761-770.
Examples
x=matrix(rnorm(200),ncol=2)
x.new=matrix(rnorm(100),ncol=2)
h=c(1,1)
f=kde_d(x.new=x.new,x.obs=x,h=h)
Likelihood cross validation bandwidth for univariate densities
Description
Likelihood cross validation bandwidth for univariate densities
Usage
lcv(x.obs, x.new = NULL)
Arguments
x.obs |
Training (observed) data |
x.new |
Evaluation data; default to x.obs |
Value
fhat: density evaluated at x.new; h: bandwidth
Author(s)
Ximing Wu xwu@tamu.edu
References
Wu, Ximing (2019), "Robust Likelihood Cross Validation for Kernel Density Estimation," Journal of Business and Economic Statistics, 37(4): 761-770.
Examples
x=rt(200,df=5)
x.new=seq(-5,5,length=100)
fit=lcv(x.obs=x,x.new=x.new)
# Mean squared errors
f0=dt(x.new,df=5)
mean((f0-fit$fhat)^2)
matplot(x.new,cbind(f0,fit$fhat),type='l')
Likelihood cross validation bandwidth for multivariate kernel densities
Description
Likelihood cross validation bandwidth for multivariate kernel densities
Usage
lcv_d(x.obs, x.new = NULL)
Arguments
x.obs |
Training (observed) data (n1 by d matrix, d>=2) |
x.new |
Evaluation data (n2 by d matrix, d>=2); default to x.obs |
Value
fhat: density evaluated at x.new; h: bandwidth
Author(s)
Ximing Wu xwu@tamu.edu
References
Wu, Ximing (2019), "Robust Likelihood Cross Validation for Kernel Density Estimation," Journal of Business and Economic Statistics, 37(4): 761-770.
Examples
# old faithful data
x=datasets::faithful
x=cbind(x[,1],x[,2])
fit=lcv_d(x.obs=x)
# evaluation data
x1=seq(min(x[,1])*.8,max(x[,1])*1.2,length=30)
x2=seq(min(x[,2])*.8,max(x[,2])*1.2,length=30)
x11=rep(x1,each=30)
x22=rep(x2,30)
fhat=kde_d(x.new=cbind(x11,x22),x.obs=x,h=fit$h)
persp(x1,x2,matrix(fhat,30,30))
Robust likelihood cross validation bandwidth for univariate densities
Description
Robust likelihood cross validation bandwidth for univariate densities
Usage
rlcv(x.obs, x.new = NULL)
Arguments
x.obs |
Training (observed) data |
x.new |
Evaluation data; default to x.obs |
Value
fhat: density evaluated at x.new; h: bandwidth
Author(s)
Ximing Wu xwu@tamu.edu
References
Wu, Ximing (2019), "Robust Likelihood Cross Validation for Kernel Density Estimation," Journal of Business and Economic Statistics, 37(4): 761-770.
Examples
x=rt(200,df=5)
x.new=seq(-5,5,length=100)
fit=rlcv(x.obs=x,x.new=x.new)
# Mean squared errors
f0=dt(x.new,df=5)
mean((f0-fit$fhat)^2)
matplot(x.new,cbind(f0,fit$fhat),type='l')
Robust likelihood cross validation bandwidth for multivariate kernel densities
Description
Robust likelihood cross validation bandwidth for multivariate kernel densities
Usage
rlcv_d(x.obs, x.new = NULL)
Arguments
x.obs |
Training (observed) data (n1 by d matrix, d>=2) |
x.new |
Evaluation data (n2 by d matrix, d>=2); default to x.obs |
Value
fhat: density evaluated at x.new; h: bandwidth
Author(s)
Ximing Wu xwu@tamu.edu
References
Wu, Ximing (2019), "Robust Likelihood Cross Validation for Kernel Density Estimation," Journal of Business and Economic Statistics, 37(4): 761-770.
Examples
# old faithful data
x=datasets::faithful
x=cbind(x[,1],x[,2])
fit=rlcv_d(x.obs=x)
# evaluation data
x1=seq(min(x[,1])*.8,max(x[,1])*1.2,length=30)
x2=seq(min(x[,2])*.8,max(x[,2])*1.2,length=30)
x11=rep(x1,each=30)
x22=rep(x2,30)
fhat=kde_d(x.new=cbind(x11,x22),x.obs=x,h=fit$h)
persp(x1,x2,matrix(fhat,30,30))