EEF.profile {boot} R Documentation

## Empirical Likelihoods

### Description

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

### Usage

```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-liklihood 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://www-stat.stanford.edu/~owen/empirical/.

### Value

A matrix with `n.t` rows. The first column contains the values of the parameter used. The second colmn 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.

[Package boot version 1.2-27 Index]