Library: | smoother |
See also: | denest denci dencb denrot denbwsel denestp |
Quantlet: | denxest | |
Description: | estimates a univariate density by kernel density estimation. |
Usage: | fh = denxest(x {,h {,K} {,v} }) | |
Input: | ||
x | n x 1 vector, the data. | |
h | scalar, bandwidth. If not given, the rule of thumb bandwidth computed by denrot is used (Silverman's rule of thumb). | |
K | string, kernel function on [-1,1] or Gaussian kernel "gau". If not given, the Quartic kernel "qua" is used. | |
v | m x 1, values of the independent variable on which to compute the density estimate. If not given, x is used. | |
Output: | ||
fh | n x 2 or m x 2 matrix, the first column is the sorted first column of x or the sorted v, the second column contains the density estimate on on the values of the first column. |
library("smoother") library("plot") ; mu = 10 si = 5 x = si*normal(200)+mu ; generate data ; fh = denxest(x) ; estimate density f = sort(x~pdfn((x-mu)/si)/si) ; true density ; ; fh = setmask(fh,"line","blue") f = setmask(f ,"line","black","thin") plot(f,fh) ; graph functions
The density estimate (blue) for a normal distribution with mean mu=10, standard deviation si=5 is pictured using Quartic kernel (default) and Silverman's rule-of-thumb bandwidth (default), together with the true density (thin black).
library("smoother") library("plot") ; mu = 10 si = 5 x = si*normal(200)+mu ; generate data ; fhe= denxest(x,3,"epa") ; estimate density fhu= denxest(x,3,"uni") ; estimate density f = sort(x~pdfn((x-mu)/si)/si) ; true density ; fhe= setmask(fhe,"line","green") fhu= setmask(fhu,"line","red") f = setmask(f ,"line","black","thin") plot(f,fhu,fhe) ; graph functions
The density estimate using the Epanechnikov kernel (green) is compared to the density estimate using the Uniform kernel (red) and the true density (thin black). In both cases, bandwidth h=3 is used.