Sequential tests that are generalizations of Page's CUSUM tests are proposed for detecting an abrupt change in any parameter, or in any collection of parameters of an autoregressive time series model. These tests accommodate nuisance parameters. They are based on large sample approximations to...

Autoregressive time series models of order p have p+2 parameters, the mean, the variance of the white noise and the p autoregressive parameters. Change in any of these over time is a sign of disturbance that is important to detect. The methods of this paper can test for change in any one of...

Asymptotic distributions of U-statistics to test for possible changes in the distribution will be derived when the change occurred. We will show that for all possible types of kernels, symmetric, antisymmetric, degenerate, non-degenerate, the test statistics are asymptotically normally...

We consider the problem of sequential change-point detection when the family of distributions is exponential, and distinguish between parameters of interest, and nuisance parameters. Likelihood ratios are used as test statistics, and their large sample approximations under the alternative...

We study the asymptotics of maximum-likelihood ratio-type statistics for testing a sequence of observations for no change in parameters against a possible change while some nuisance parameters remain constant over time. We obtain extreme value as well as Gaussian-type approximations for the...