A SELECTION OF INITIAL ESTIMATOR WHEN COMPUTING MAXIMUM LIKELIHOOD ESTIMATE BASED ON BINARY RESPONSE DATA : Dedicated to Professor Fumi-Yuki Maeda on his 60th birthday

An estimator, called initial estimator, is proposed for the complementary log-log model when the binary response data are observed. It is shown that this estimation can be used as an estimator of the true parameter and that this estimator can be adopted as an initial value when computing the value of maximum likelihood estimate. It is also shown that in a simulation study, our proposed initial estimator has smaller bias than that of maximum likelihood estimator for in a case when the size of sample is small.