chorussell.simp: Simplifies the candidates to be considered in 'chorussell'
In conroylau/lpinfer: An R Package for Inference in Linear Programs

chorussell.simp

R Documentation

Simplifies the candidates to be considered in `chorussell`

Description

This function simplifies the list of candidates to be considered in the optimization problem in the chorussell function. In particular, because

\mathbf{1}\left[\sqrt{n}\left(\hat{\theta}_{\rm lb}^b - \hat{\theta}_{\rm lb}\right) \leq c_{\rm lb}\right] \geq \mathbf{1}\left[\sqrt{n}\left(\hat{\theta}^b_{\rm lb} - \hat{\theta}_{\rm lb}\right) \leq c_{\rm lb} \quad \mathrm{ and } \quad -c_{\rm ub} \leq \sqrt{n} \left(\hat{\theta}^b_{\rm ub} - \hat{\theta}_{\rm ub} + \Delta\right) \right],

the values of c_{\rm lb} that satisfy

\frac{1}{B}\sum^B_{b=1} \mathbf{1} \left[\sqrt{n}\left(\hat{\theta}_{\rm lb}^b - \hat{\theta}_{\rm lb}\right) \leq c_{\rm lb}\right] < 1 - \alpha

will be removed from the set of the values under consideration. Similarly, the list of c_{\rm ub} that satisfy

\frac{1}{B}\sum^B_{b=1} \mathbf{1} \left[- \sqrt{n}\left(\hat{\theta}_{\rm ub}^b - \hat{\theta}_{\rm ub}\right) \leq c_{\rm lb}\right] < 1 - \alpha

will be removed from the set of the values under consideration.

Usage

chorussell.simp(lb.can1, lb.can2, ub.can1, ub.can2, progress)

Arguments

`lb.can1`	The vector of values that corresponds to `\sqrt{n}\left(\hat{\theta}^b_{\rm lb} - \hat{\theta}_{\rm lb}\right)`.
`lb.can2`	The vector of values that corresponds to `\sqrt{n}\left(\hat{\theta}^b_{\rm lb} - \hat{\theta}_{\rm lb} - \Delta \right)`.
`ub.can1`	The vector of values that corresponds to `\sqrt{n}\left(\hat{\theta}^b_{\rm ub} - \hat{\theta}_{\rm ub}\right)`.
`ub.can2`	The vector of values that corresponds to `\sqrt{n}\left(\hat{\theta}^b_{\rm ub} - \hat{\theta}_{\rm ub} + \Delta \right)`.
`progress`	The boolean variable for whether the progress bars should be displayed. If it is set as `TRUE`, the progress bars will be displayed while the code is running.