Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties. Apart from histograms, other types of density estimators include parametric, spline, wavelet and Fourier series. Kernel density estimators were first introduced in the scientific literature for univariate data in the 1950s and 1960s[1][2] and subsequently have been widely adopted. It was soon recognised that analogous estimators for multivariate data would be an important addition to multivariate statistics. Based on research carried out in the 1990s and 2000s, multivariate kernel density estimation has reached a level of maturity comparable to its univariate counterparts.[3][4][5]
- ^ Rosenblatt, M. (1956). "Remarks on some nonparametric estimates of a density function". Annals of Mathematical Statistics. 27 (3): 832–837. doi:10.1214/aoms/1177728190.
- ^ Parzen, E. (1962). "On estimation of a probability density function and mode". Annals of Mathematical Statistics. 33 (3): 1065–1076. doi:10.1214/aoms/1177704472.
- ^ Wand, M.P; Jones, M.C. (1995). Kernel Smoothing. London: Chapman & Hall/CRC. ISBN 9780412552700.
- ^ Simonoff, J.S. (1996). Smoothing Methods in Statistics. Springer. ISBN 9780387947167.
- ^ Chacón, J.E. and Duong, T. (2018). Multivariate Kernel Smoothing and Its applications. Chapman & Hall/CRC. ISBN 9781498763011.
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