File:Kernel density estimation, comparison between rule of thumb and solve-the-equation bandwidth.png
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Summary
| Description | |
| Date | |
| Source |
 This diagram was created with MATLAB. |
| Author | Kernel estimator |
|
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The Matlab script for this example uses kde.m and is given below.
% Data
randn('seed',1) % Used for reproducibility
data = [randn(100,1)-10; randn(100,1)+10]; % Two Normals mixed
% True
phi = @(x) exp(-.5*x.^2)/sqrt(2*pi); % Normal Density
tpdf = @(x) phi(x+10)/2+phi(x-10)/2; % True Density
% Kernel
h = std(data)*(4/3/numel(data))^(1/5); % Bandwidth estimated by Silverman's Rule of Thumb
kernel = @(x) mean(phi((x-data)/h)/h); % Kernel Density
kpdf = @(x) arrayfun(kernel,x); % Elementwise application
% Plot
figure(2), clf, hold on
x = linspace(-25,+25,1000); % Linear Space
plot(x,tpdf(x)) % Plot True Density
plot(x,kpdf(x)) % Plot Kernel Density with Silverman's Rule of Thumb
kde(data) % Plot Kernel Density with Solve-the-Equation Bandwidth
#The same code with R language
#` Data
set.seed(1) #Used for reproducibility
data = c(rnorm(100,-10,1),rnorm(100,10,1)) #Two Normals mixed
#` True
phi = function(x) exp(-.5*x^2)/sqrt(2*pi) #Normal Density
tpdf = function(x) phi(x+10)/2+phi(x-10)/2 #True Density
#` Kernel
h = sd(data)*(4/3/length(data))^(1/5) #Bandwidth estimated by Silverman's Rule of Thumb
Kernel2 = function(x) mean(phi((x-data)/h)/h) #Kernel Density
kpdf = function(x) sapply(x,Kernel2) #Elementwise application
#` Plot
x=seq(-25,25,length=1000) #Linear Space
plot(x,tpdf(x),type="l",ylim=c(0,0.23),col="red") #Plot True Density
par(new=T)
plot(x,kpdf(x),type="l",ylim=c(0,0.23),xlab="",ylab="",axes=F) #Plot Kernel Density with Silverman's Rule of Thumb
Licensing
User:Kernel estimator, the copyright holder of this work, hereby publishes it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
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Original upload log
Transferred from en.wikipedia to Commons using For the Common Good.
The original description page was here. All following user names refer to en.wikipedia.
| Date/Time | Dimensions | User | Comment |
|---|---|---|---|
| 15:47, 19 April 2016 | 733 × 561 (28,809 bytes) | w:en:Kernel estimator (talk | contribs) | author: kernel estimator source: created by kernel estimator using the Matlab code on Wikipedia URL: N/A |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:39, 26 October 2018 | | 733 × 561 (28 KB) | Jumpow | Transferred from en.wikipedia: see original upload log above |
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