eel (version 1.1)

prime_image_est: Calculating prime-image based on similarity mapping for parameters defined by estimating equations

Description

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

Usage

prime_image_est(theta_tilda, theta, x, equation)
"prime_image_est"(theta_tilda, theta, x, equation)

Arguments

theta_tilda

The maximum empirical likelihood estimates for parameters defined by estimating equations.

theta

The value to be evaluated.

x

Data Matrix.

equation

The estimating equation by which the parameters are defined, must be put as a function of theta.

Value

The function returns a vector, with the same dimension 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_est,EEL_est,prime_image

Examples

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