MKLE-package {MKLE}R Documentation

Maximum kernel likelihood estimation

Description

Computes the maximum kernel likelihood estimator using fast fourier transforms.

Details

Package: MKLE
Type: Package
Version: 0.03
Date: 2007-08-14
License: GNU

The maximum kernel likelihood estimator is defined to be the value $hattheta_h$ that maximizes the estimated kernel likelihood based on the general location model, $$f(x|theta) = f_{0}(x - theta).$$

This model assumes that the mean associated with $f_0$ is zero which of course implies that the mean of $X_i$ is $theta$. The kernel likelihood is the estimated likelihood based on the above model using a kernel density estimate, $hat f(.|h,X_1,...,X_n)$, and is defined as $$hat L(theta|X_1,...,X_n) = prod_{i=1}^n hat f(X_{i}-(bar{X}-theta)|h,X_1,...,X_n).$$

The resulting estimator therefore is an estimator of the mean of $X_i$.

Author(s)

Thomas Jaki

Maintainer: Thomas Jaki <jaki.thomas@gmail.com>

References

Jaki T., West R. W. (2007) Maximum kernel likelihood estimation. Submitted to textit{Journal of Computational and Graphical Statistics}.

Silverman, B. W. (1986), textit{Density Estimation for Statistics and Data Analysis}, Chapman & Hall, 2nd ed.

Examples

data(state)
mkle(state$CRIME)

[Package MKLE version 0.03 Index]