\name{asym.spenv}
\alias{asym.spenv}
\title{Asyptotic covariance of vec(beta) for a fitted sparse envelope model}
\description{
  This function compute the asyptotic covariance of vec(beta) and asymptotic standard error for elements in beta for a fiteed sparse envelope model. 
  }
\usage{
       ModelOutput = asym.spenv(object)
}

\arguments{
  \item{object}{A fitted spenv object.}
}

\value{
  \item{covMatrix}{The asymptotic covariance of vec(beta). An rp by rp matrix. The covariance matrix returned are asymptotic.  For the actual standard errors, multiply by 1/n.}
  \item{asySE}{The asymptotic standard error for elements in beta under the envelope model.  An r by p matrix.  The standard errors returned are asymptotic, for actual standard errors, multiply by 1/sqrt(n).}
  \item{ratio}{The asymptotic standard error ratio of the standard multivariate linear regression estimator over the envelope estimator, for each element in beta.  An r by p matrix.}
}
 
\references{
Su Z, Zhu G, Chen X, Yang Y. Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression. Biometrika. 2016 Sep 1;103(3):579-93.
} 

\author{Zhihua Su\cr Maintainer: Guangyu Zhu \email{gzhu22@ufl.edu}}

\seealso{\code{choose_env} for choosing the dimension of envelope subspace.}