The lower bound method in probit regression
The lower bound principle consists of replacing the second derivative matrix of the log-likelihood by a global lower bound in the Loewner ordering. This bound is then used in the NewtonRaphson iteration instead of the Hessian matrix leading to a monotonically converging sequence of iterates. In this note we apply this principle to probit regression as an example of a generalized linear model for which observed and expected information matrix do not coincide. This note also points out that it is not sufficient to use a bound for the expected value of the Hessian matrix as has been suggested recently in the context of generalized linear models.
lower bound method generalized linear model probit link function and probit regression quadratic approximation of log-likelihood