chorussell.simp: Simplifies the candidates to be considered in 'chorussell'

In conroylau/lpinfer: An R Package for Inference in Linear Programs

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}≤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

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. 23, 2022, 9:21 a.m.