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. Kernel density estimators were first introduced in the scientific literature for univariate data in the 1950s and 1960s by [1][2] and subsequently have been widely adopted. It was soon recognised that analagous estimators for multivariate data would be an important addition to multivariate statistics.
Motivation
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.
- ^ Parzen, E. (1962). "On estimation of a probability density function and mode". Annals of Mathematical Statistics. 33: 1065–1076. doi:10.1214/aoms/1177704472.