Logistic and Nonlogistic Density Functions in Binary Regression with Nonstochastic Covariates

A binary random variable depends on nonstochastic covariates through a density function. The equations that determine the maximum likelihood estimators of the parameters are intractable and difficult to solve iteratively. We develop modified maximum likelihood estimators for both logistic and nonlo‐gistic densities. These estimators are explicit functions of sample observations and are, therefore, easy to compute. They are asymptotically fully efficient and, for small samples, are almost fully efficient. The appropriateness of the logistic density function is also discussed.