beta.product: Computes vector products
In conroylau/lpinfer: An R Package for Inference in Linear Programs

beta.product

R Documentation

Computes vector products

Description

This function computes the product of the two vectors. This is used in the sigma.summation function that computes the asymptotic variance estimator.

Usage

beta.product(beta, beta.obs.hat, pbar, progress, eval.count)

Arguments

`beta`	A bootstrap estimator `beta.obs`.
`beta.obs.hat`	The sample estimator `\widehat{\bm{\beta}}_{\mathrm{obs}, n}` based on the given information in `lpmodel` (and `data` if applicable).
`pbar`	The progress bar object.
`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.
`eval.count`	The count for the number of times the `future_map` function has been called. If this object is zero, it means that the `future_map` function is being called for the first time in this subprocedure. Otherwise, it means that the `future_map` function has been called for more than once. This situation typically refers to the situations where there are some errors in the first time of the replications.

Details

Denote \bm{\beta} and \hat{\bm{\beta}}_{\rm obs} as the n \times 1 vectors beta and beta.obs.hat respectively. This function returns the n \times n matrix \widetilde{\bm{\beta}}\widetilde{\bm{\beta}}' where \widetilde{\bm{\beta}} is defined as \widetilde{\bm{\beta}} \equiv \bm{\beta} - \widehat{\bm{\beta}}_{\rm obs}.