How to Estimate Kernel Smoothing Density

Kernel Smoothing Density is an important tool for statistical analysis.

Kernel Smoothing Density is a technique for estimating the regression function or probability density function of a series of random numbers. This estimation is very important in many types of statistical analysis. This type of calculation can be tedious if done by hand, as there may be hundreds or even thousands of data points. however, with the commercial software package MATLAB, it is possible to make this estimation using a series of short commands.

Things You'll Need

• Knowledge of MATLAB

Instructions

1. Create a vector with a series of values. As an example, the command

   x = [randn(30,1); 5+randn(30,1)];

   Will create a vector with 60 values: 30 random numbers with a normal distribution, and 30 numbers with a normal distribution, added by 5.

2. Make the Kernel Smoothing estimate using the command

   [f,xi] = ksdensity(x);

   This will produce a vector of values 'f' valuated at the points 'xi'.

3. Plot the Kernel Smoothing Density to investigate its behavior using the command

   plot(xi,f);

   This will plot the density over a range of values from the initial vector of values 'x'.

Tips & Warnings

• If you do not have access to MATLAB, the same calculations can be done using GNU Octave, an open-source numerical computation system with similar syntax to MATLAB.

References

• Max Planck Institute for Molecular Genetics: Introduction to Kernel Smoothing
• MathWorks: Kernel Smoothing Density Estimate

Resources

• GNU Octave