ESTIMATION OF CHANGE POINT IN BINOMIAL RANDOM VARIABLES USING NEURAL NETWORKS

Abstract

Statistically, change point is the location or the time point such that observations follow one distribution up to the point and then another afterwards. Change point problems are encountered in our daily life and in disciplines such as economics, nance, medicine, geology, literature among others. Change-point analysis is a powerful tool for determining whether a change has taken place. In this study, change point in binomial random variables whose mean is dependent on explanatory variables is investigated. It is assumed that there was only a single change point in the data. Arti cial neural networks are used to estimate the conditional means. Compared with the generalized linear methods the arti cial neural network gave better probability estimates. The consistency and the asymptotic distribution of the change point estimator is also investigated, and is found to be asymptotically normally distributed. The limiting distribution of the network based likelihood ratio statistic when change exists is derived and critical regions obtained. Simulated data is used to investigate the power of the test. The test is found to be more powerful when the change is near the center of the data than when it in the edges. The power of the test was found to be a ected by the magnitude of the change. The higher the size of the change the higher the chance of detecting it. The power of the test is also found to increase as the size of the sample. In the analysis of real data the change point was found to correspond with the LD50.