# VARbeta.fun: Calculate the covariance matrix of the \hat beta vector. In NHPoisson: Modelling and Validation of Non Homogeneous Poisson Processes

## Description

This function estimates the covariance matrix of the ML estimators of the β parameters, using the asymptotic distribution and properties of the ML estimators.

## Usage

 1 VARbeta.fun(covariates, lambdafit) 

## Arguments

 covariates Matrix of covariates (each column is a covariate). lambdafit Numeric vector, the fitted PP intensity \hat λ(t).

## Details

The covariance matrix is calculated as the inverse of the negative of the hessian matrix. The inverse of the matrix is calculated using the solve function. If this function leads to an error in the calculation, the inverse is calculated via its Cholesky decomposition. If this option also fails, the covariance matrix is not estimated and a matrix of dimension 0 \times 0 is returned.

## Value

 VARbeta  Coariance matrix of the \hat β vector. It has an attribute, called 'CalMethod' which shows the method used to calculate the inverse of the matrix: 'Solve function', 'Cholesky' or 'Not possible'.

## Note

The function fitPP.fun calls this function.

## References

Casella, G. and Berger, R.L., (2002). Statistical inference. Brooks/Cole.

Cebrian, A.C., Abaurrea, J. and Asin, J. (2015). NHPoisson: An R Package for Fitting and Validating Nonhomogeneous Poisson Processes. Journal of Statistical Software, 64(6), 1-24.

CItran.fun, CIdelta.fun
 1 2 3 4 lambdafit<-runif(100,0,1) X<-cbind(rep(1,100),rnorm(100),rnorm(100)) aux<-VARbeta.fun(covariates=X, lambdafit=lambdafit)