On the Fisher information in type-I censored and quantal response data

The paper presents some results on the Fisher information for type-I censored data and for quantal response data. It is shown that for one-parameter family, the Fisher information for type-I censoring is always greater or equal than the Fisher information for quantal response, for equal censoring times. A numerical comparison is made for the exponential and Weibull distributions and it is shown that if the censoring time does not exceed the mean lifetime, then the gain in information for type-I censoring over the quantal-type censoring is quite small. For quantal response, the Fisher information matrix IF is derived for a location-scale family. It is shown how to choose optimally the censoring times for an extreme-value distribution in order to maximize the determinant of the information matrix. Also the log-linear model Y = log [tau] = [beta]x + [sigma]Z is investigated where Z has a (0, 1)-extreme-value distribution, under type-I censoring. If [sigma] is known and the covariate vectors x form a full-rank orthogonal matrix, simple formulas can be derived for IF, its spectrum and trace. Also some properties of the observed information are established for this model. For [sigma] unknown, a closed expression is derived for the sum of the asymptotic variances of maximum likelihood estimators of [beta]i.