eel (version 1.1)

prime_image: Calculating prime-image based on similarity mapping for the mean

Description

The function calculates the prime image of the given point based on the similarity mapping defined in the EEL calculaiton.

Usage

prime_image(theta_tilda, theta, x)
"prime_image"(theta_tilda,theta,x)

Arguments

theta_tilda

Sample mean or the maximum empirical likelihood estimate of the estimating equaitons.

theta

Value to be evaluated.

x

Data matrix.

Value

The function returns a vector, with the same length as the mean, representing the prime image of the point theta, based on the similarity mapping defind in EEL calculation.

Details

The prime image was found by solving the equation $$f(\zeta'')=\zeta'.$$ See the reference paper for details.

References

Tsao, M. (2013). Extending the empirical likelihood by domain expansion. The Canadian Journal of Statistics, 41 (2), 257-274.

Tsao, M., & Wu, F. (2013). Empirical likelihood on the full parameter space. Annals of Statistics, 0 (00), 1-21. doi: 10.1214/13-AOS1143

See Also

EEL,exp_factor,eel-package,prime_image_est

Examples

x=rnorm(50,6,2)
# find the prime image of true mean
prime_image(theta_tilda=mean(x),theta=6,x=x)