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In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y .
Èlizbar Nadaraya is a Georgian mathematician who is currently a Full Professor and the Chair of the Theory of Probability and Mathematical Statistics at the Tbilisi State University. [1] He developed the Nadaraya-Watson estimator along with Geoffrey Watson , which proposes estimating the conditional expectation of a random variable as a ...
The standard Nadaraya–Watson estimator for a nonparametric model takes form ^ = ^ [()] ^ [()], for a suitable choice of the kernel K and the bandwidth h. Both expectations here can be estimated using the same technique as in the previous method.
A kernel smoother is a statistical technique to estimate a real valued function: as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single parameter.
Kernel regression estimates the continuous dependent variable from a limited set of data points by convolving the data points' locations with a kernel function—approximately speaking, the kernel function specifies how to "blur" the influence of the data points so that their values can be used to predict the value for nearby locations.
In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable.
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