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

## Description

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

\mathbf{1}≤ft[√{n}≤ft(\hat{θ}_{\rm lb}^b - \hat{θ}_{\rm lb}\right) ≤q c_{\rm lb}\right] ≥q \mathbf{1}≤ft[√{n}≤ft(\hat{θ}^b_{\rm lb} - \hat{θ}_{\rm lb}\right) ≤q c_{\rm lb} \quad \mathrm{ and } \quad -c_{\rm ub} ≤q √{n} ≤ft(\hat{θ}^b_{\rm ub} - \hat{θ}_{\rm ub} + Δ\right) \right],

the values of c_{\rm lb} that satisfy

\frac{1}{B}∑^B_{b=1} \mathbf{1} ≤ft[√{n}≤ft(\hat{θ}_{\rm lb}^b - \hat{θ}_{\rm lb}\right) ≤q c_{\rm lb}\right] < 1 - α

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

\frac{1}{B}∑^B_{b=1} \mathbf{1} ≤ft[- √{n}≤ft(\hat{θ}_{\rm ub}^b - \hat{θ}_{\rm ub}\right) ≤q c_{\rm lb}\right] < 1 - α

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

## Usage

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

## Arguments

 lb.can1 The vector of values that corresponds to √{n}≤ft(\hat{θ}^b_{\rm lb} - \hat{θ}_{\rm lb}\right). lb.can2 The vector of values that corresponds to √{n}≤ft(\hat{θ}^b_{\rm lb} - \hat{θ}_{\rm lb} - Δ \right). ub.can1 The vector of values that corresponds to √{n}≤ft(\hat{θ}^b_{\rm ub} - \hat{θ}_{\rm ub}\right). ub.can2 The vector of values that corresponds to √{n}≤ft(\hat{θ}^b_{\rm ub} - \hat{θ}_{\rm ub} + Δ \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.

## Value

Returns the list of updated candidates of lower bounds and upper bounds.

 lb The updated list of candidates of lower bounds. ub The updated list of candidates of upper bounds.

conroylau/lpinfer documentation built on Oct. 7, 2020, 5:45 a.m.