This article studies the problem of testing and locating changepoints in stochastic ordering. We propose a sequential process to detect the changepoints from two multinomial distributions. We also obtain the maximum likelihood estimators of two multinomial probability vectors under the assumption that the cumulative distributions have a changepoint. Asymptotically unbiased Akaike's information criterion is used to estimate the changepoints of two discrete probability distributions. Finally, we demonstrate our procedure by studying a data set pertaining to average daily insulin dose from the Boston Collaborative Drug Surveillance Program and locate the changepoints in stochastic ordering.
- Chi-bar square distribution
- Information criterion
- Isotonic regression
- Maximum likelihood estimate (MLE)
- Multinomial distribution