Limit Theorems for Fisher-Score Change Processes

Change analysis concerned with fluctuation of the data in accordance with probability distributions fitted to a whole sample from nonstationarity changes in the parameters of probability distributions. To detect change over time in a sequence of observations one forms for various transformations of the data sample change processes on 0,1 the transformations are called data score functions . One can choose non-parametric score functions which detect changes of location, scale, skewness, etc. in the probability distribution of the observation When a parametric model is available for the distribution of each observation one can detect changes in the parameter values by transforming the data by parametric score functions which we call Fisher-score functions. This paper studies the asymptotic distributions under the null hypothesis of no change of Fisher-score change processes which are cusums of scored data. They are related to cuscore processes or cumulative score processes. Fisher-score change processes Limit theorems.