Method for Returning Covariance of Fixed Parameters for tcensReg S3 Objects
# S3 method for tcensReg
vcov(object, logsigma = FALSE, ...)Object of class tcensReg
Logical indicator of whether to return standard deviation as logsigma or sigma. Default is FALSE returning sigma
Additional optional parameters
Numeric matrix of variance covarince values
If logsigma=TRUE, the default variance covariance matrix is returned.
Otherwise if the parameter sigma is desired then logsigma=FALSE, and
we use the multivariate delta method to find these values as described below:
Original Asymptotic Result: $$\theta=(\beta_{1}, \dots, \beta_{(p-1)}, \log(\sigma))^{T}\sim N_{p}(\hat{\theta}, \hat{\Sigma}_{\theta})$$
Transformed Parameters: $$g(\theta)=(\beta_{1}, \dots, \beta_{(p-1)}, \exp\{\log(\sigma)\})^{T}\sim N_{p}(g(\hat{\theta}), \nabla_{g(\theta)}^{T}\hat{\Sigma}_{\theta}\nabla_{g(\theta)})$$
The gradient vector is defined as $$\nabla_{g(\theta)}=diag(1_{p-1}, \log(\sigma)\exp\{\log(\sigma)\})_{p\times p}$$