MKLE (version 0.05)

MKLE-package: Maximum kernel likelihood estimation

Description

Computes the maximum kernel likelihood estimator using fast fourier transforms.

Details

Package:	MKLE
Type:	Package
Version:	0.05
Date:	2008-05-02
License:	GPL

The maximum kernel likelihood estimator is defined to be the value \(\hat \theta\) 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, \(\hat f(.|h,X_1,\dots,X_n)\), and is defined as $$\hat L(\theta|X_1,\dots,X_n) = \prod_{i=1}^n \hat f(X_{i}-(\bar{X}-\theta)|h,X_1,\dots,X_n).$$

The resulting estimator therefore is an estimator of the mean of \(X_i\).

References

Jaki T., West R. W. (2008) Maximum kernel likelihood estimation. Journal of Computational and Graphical Statistics Vol. 17(No 4), 976-993.

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

Examples

# NOT RUN {
data(state)
mkle(state$CRIME)
# }