Statistical Analysis with Missing Data., 3rd Edition

9Large-Sample Inference Based on Maximum Likelihood Estimates

9.1 Standard Errors Based on The Information Matrix

We noted in Chapter 6 that large-sample maximum likelihood (ML) inferences can be based on Approximation 6.1, namely that

(9.1)

where C is an estimate of the d × d covariance matrix of , for example,

(9.2)

the inverse of the observed information evaluated at , or

(9.3)

the inverse of the expected information evaluated at , or

(9.4)

the sandwich estimator. The estimate (9.2) is computed as part of the Newton–Raphson algorithm for ML estimation, and (9.3) is computed as part of the scoring algorithm. When the expectation–maximization (EM) algorithm or one of the variants described in Chapter 8 is used for ML estimation, additional steps are needed to compute standard errors ...