Estimation of exponential regression parameters using binary data

Exponential regression model is important in analyzing data from heterogeneous populations. In this paper we propose a simple method to estimate the regression parameters using binary data. Under certain design distributions, including ellipticaily symmetric distributions, for the explanatory variables, the estimators are shown to be consistent and asymptotically normal when sample size is large. For finite samples, the new estimates were shown to behave reasonably well. They are competitive with the maximum likelihood estimates and more importantly, according to our simulation results, the cost of CPU time for computing new estimates is only 1/7 of that required for computing the usual maximum likelihood estimates. We expect the savings in CPU time would be more dramatic with larger dimension of the regression parameter space.