Statistics is a field of quantitative analysis concerned with quantifying uncertainty. The main building block of statistical analysis is a random variable. A random variable is a mathematics function which assigns a numerical value to each possible value of the variable of interest. The complete behaviour of a random variable is contained in its distribution function. For continuous random variables, the partial derivative of the distribution function is known as probability density function or pdf. So density estimation is a fundamental question in statistics.
Kernel density estimation is one of the most popular techniques for density estimation. It can be viewed as a generalisation of histogram density estimation with improved statistical properties.
Motivation
Kernel density estimators were first introduced in the scientific literature for univariate data by [1]
References
- ^ Rosenblatt, M. (1956). "Remarks on some nonparametric estimates of a density function". Annals of Mathematical Statistics. 27: 832–837. doi:10.1214/aoms/1177728190.