beta.star.qp: Computes the starred components of \widehat{\bm{beta}}

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

Computes the starred components of \widehat{\bm{\beta}}

Description

This function computes the vector \widehat{\bm{\beta}}_n^\star for the case where d<p in the fsst procedure.

Usage

beta.star.qp(
  data,
  lpmodel,
  beta.tgt,
  weight.mat,
  beta.obs.hat,
  beta.sigma,
  solver
)

Arguments

data	An data frame or a matrix.
lpmodel	The lpmodel object.
beta.tgt	The value to be tested.
weight.mat	The weighting matrix for the fsst procedure.
beta.obs.hat	The sample estimator \widehat{\bm{\beta}}_{\mathrm{obs}, n} based on the given information in lpmodel (and data if applicable).
beta.sigma	The variance estimator of \bm{\beta}_{\rm obs}.
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

This corresponding to solving the following quadratic program

\min_{x \in \mathbf{R}^d} \,\, \left(\hat{\beta}_{{\rm obs}, n} - A_{\rm obs} x\right)' \hat{\Xi} \left(\hat{\beta}_{{\rm obs}, n} - A_{\rm obs} x\right) \quad \mathrm{s.t. } \quad A_{\rm shp} x = \beta_{\rm shp} \quad \mathrm{ and } \quad A_{\rm tgt} x = \beta_{\rm tgt}

in the fsst procedure.

Value

Returns the following objects:

beta.star	The vector \widehat{\bm{\beta}}_n^\star.
x	The optimal point.
status	The status of the optimization problem.

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