FIXED SIZE CONFIDENCE-REGIONS FOR PARAMETERS OF A LOGISTIC-REGRESSION MODEL

Let (X(i), Y(i)) be independent, identically distributed observations that satisfy a logistic regression model; that is, for each i, log[P(Y(i) = 1\X(i))/P(Y(i) = 0\X(i))] = X(i)(T)beta0, where Y(i) is-an-element-of {0, 1}, X(i) is-an-element-of (R)p and beta0 is-an-element-of R(p) is the unknown parameter vector of the model. The marginal distribution of the covariate vectors X(i) is assumed to be unknown. Sequential procedures for constructing fixed size and fixed proportional accuracy confidence regions for beta0 are proposed and shown to be asymptotically efficient as the size of the region becomes small.