mig_loglik_hessian

This function returns the hessian, i.e., the matrix of
second derivatives of the log likelihood with respect to the
argument <code>x</code>.

internal

Provides utilities for estimation for the multivariate inverse Gaussian distribution of Minami (2003) <doi:10.1081/STA-120025379>, including random vector generation and explicit estimators of the location vector and scale matrix. The package implements kernel density estimators discussed in Belzile, Desgagnes, Genest and Ouimet (2024) <doi:10.48550/arXiv.2209.04757> for smoothing multivariate data on half-spaces.

Leo Belzile

Multivariate Inverse Gaussian Distribution

Frederic Ouimet

mig_loglik_hessian function

<dl><dt>x</dt>
<dd><code>n</code> by <code>d</code> matrix of quantiles</dd>
<dt>beta</dt>
<dd><code>d</code> vector \(\boldsymbol{\beta}\) defining the half-space through \(\boldsymbol{\beta}^{\top}\boldsymbol{\xi}&gt;0\)</dd>
<dt>xi</dt>
<dd><code>d</code> vector of location parameters \(\boldsymbol{\xi}\), giving the expected value</dd>
<dt>Omega</dt>
<dd><code>d</code> by <code>d</code> positive definite scale matrix \(\boldsymbol{\Omega}\)</dd></dl>

Arguments

Hessian of the MIG log likelihood with respect to data — mig_loglik_hessian

<dl>

<dt>x</dt>
<dd><code>n</code> by <code>d</code> matrix of quantiles</dd>


<dt>beta</dt>
<dd><code>d</code> vector \(\boldsymbol{\beta}\) defining the half-space through \(\boldsymbol{\beta}^{\top}\boldsymbol{\xi}&gt;0\)</dd>


<dt>xi</dt>
<dd><code>d</code> vector of location parameters \(\boldsymbol{\xi}\), giving the expected value</dd>


<dt>Omega</dt>
<dd><code>d</code> by <code>d</code> positive definite scale matrix \(\boldsymbol{\Omega}\)</dd>

</dl>

mig_loglik_hessian: Hessian of the MIG log likelihood with respect to data

Description

Usage

Value

Arguments