Abstract
Suppose that y is a binary variable which takes the values 1 or 0, and P[y=1] is given as a function of a K-dimensional vector x. Dividing the space of x into two regions A and B, so that P[y=1|x]>1/2 if x∈A and P[y=1|x]<1/2 if x∈B, is important for some fields such as neural network computers.
Nawata [1990a, b] proposed a new estimation method which is based on grouping. This paper shows that Nawata's grouping method can be used for the problem mentioned above. In the estimation, the sample space of the independent variables is divided into N cells so that the size of each cell goes to zero as the number of observations goes to infinity. Each cell is labeled as 1 if more than half of the yt's in the cell are 1, and 0 otherwise. The probit maximum likelihood method is then applied to these newly-defined values.
