Computes the maximum kernel likelihood estimator using fast fourier transforms.
Thomas Jaki
Maintainer: Thomas Jaki <jaki.thomas@gmail.com>
| Package: | MKLE |
| Type: | Package |
| Version: | 1.01 |
| Date: | 2023-08-21 |
| 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 \(X_i\).
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.