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.