dkqs.qlp: Formulates and solves the linear and quadratic programs in...

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

Formulates and solves the linear and quadratic programs in the dkqs procedure

Description

This function formulates the matrices and vectors used in the DKQS test and solves the quadratic programs (4) or linear programs (5) and (6) in Torgovitsky (2019).

Usage

dkqs.qlp(lpmodel, beta.tgt, beta.obs.hat, tau, problem, n, solver)

Arguments

lpmodel	An lpmodel object.
beta.tgt	The value to be tested.
beta.obs.hat	The value of sample \hat{\bm{\beta}}_{\mathrm{obs}} from the lpmodel object.
tau	The value of the tuning parameter \tau in the DKQS procedure. This can be a vector.
problem	The problem that the function will be solved.
n	Number of observations for the data.
solver	The name of the linear and quadratic programming solver that is used to obtain the solution to linear and quadratic programs. The solvers supported by this package are cplexAPI, gurobi, limSolve and Rcplex.

Details

The argument problem must be one of the followings:

• test — this computes the solution to the quadratic program that solves the test statistic, i.e. quadratic program (4) in Torgovitsky (2019)

• cone — this computes the solution to the quadratic program for the bootstrap test statistics, i.e. quadratic program (5) in Torgovitsky (2019)

• tau — this computes the value of tau based on the procedure suggested by Kamat (2018), i.e. linear program (6) in Torgovitsky (2019)

Value

Returns the optimal point and optimal value.

objval	The optimal value.
x	The optimal point.
lb0	The logical lower bound.
ub0	The logical upper bound.

conroylau/lpinfer documentation built on Oct. 25, 2024, 4 a.m.