Matrix repair

(Nov 25, 2019)

When fitting a statistical model we want two things as a minimum:

  1. The parameter estimates, e.g. the maximum-likelihood estimates (MLEs), and
  2. The estimated variance-covariance matrix, \(\hat V\), for those estimates.

We can get both from the log-likelihood: the MLEs maximise the value of the log-likelihood function, and an approximation for the covariance matrix comes from inverting the negative information matrix, \(\mathcal J\), i.e. the matrix of second partial derivatives evaluated at the MLEs. However, the limitations of computer arithmetic can sometimes get in the way, as shown in the information matrix in Figure 1:

Figure 1. Information matrix, \(\mathcal J\), for a five-parameter model. Only…

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Tags: information matrix, covariance matrix

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