# EEF.profile: Empirical Likelihoods In boot: Bootstrap Functions (Originally by Angelo Canty for S)

## Description

Construct the empirical log likelihood or empirical exponential family log likelihood for a mean.

## Usage

 ```1 2 3 4``` ```EEF.profile(y, tmin = min(y) + 0.1, tmax = max(y) - 0.1, n.t = 25, u = function(y, t) y - t) EL.profile(y, tmin = min(y) + 0.1, tmax = max(y) - 0.1, n.t = 25, u = function(y, t) y - t) ```

## Arguments

 `y` A vector or matrix of data `tmin` The minimum value of the range over which the likelihood should be computed. This must be larger than `min(y)`. `tmax` The maximum value of the range over which the likelihood should be computed. This must be smaller than `max(y)`. `n.t` The number of points between `tmin` and `tmax` at which the value of the log-likelihood should be computed. `u` A function of the data and the parameter.

## Details

These functions calculate the log likelihood for a mean using either an empirical likelihood or an empirical exponential family likelihood. They are supplied as part of the package `boot` for demonstration purposes with the practicals in chapter 10 of Davison and Hinkley (1997). The functions are not intended for general use and are not supported as part of the `boot`package. For more general and more robust code to calculate empirical likelihoods see Professor A. B. Owen's empirical likelihood home page at the URL http://statistics.stanford.edu/~owen/empirical/.

## Value

A matrix with `n.t` rows. The first column contains the values of the parameter used. The second column of the output of `EL.profile` contains the values of the empirical log likelihood. The second and third columns of the output of `EEF.profile` contain two versions of the empirical exponential family log-likelihood. The final column of the output matrix contains the values of the Lagrange multiplier used in the optimization procedure.

Angelo J. Canty

## References

Davison, A. C. and Hinkley, D. V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

boot documentation built on July 30, 2017, 5:01 p.m.