Minimax Optimality of CUSUM for an Autoregressive Model

Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others the change is in the unconditional distribution. Some models include an observation before the first possible change time — others not. Earlier and new CUSUM type methods are given and minimax optimality is examined. For the conditional model with an observation before the possible change there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.Autoregressive; Change point; Monitoring; Online detection

Minimax Optimality of CUSUM for an Autoregressive Model

Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others the change is in the unconditional distribution. Some models include an observation before the first possible change time — others not. Earlier and new CUSUM type methods are given and minimax optimality is examined. For the conditional model with an observation before the possible change there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.This work was partially supported by the Swedish Civil Contingencies Agency

Frontiers in statistical quality control 11

The main focus of this edited volume is on three major areas of statistical quality control: statistical process control (SPC), acceptance sampling and design of experiments. The majority of the papers deal with statistical process control, while acceptance sampling and design of experiments are also treated to a lesser extent. The book is organized into four thematic parts, with Part I addressing statistical process control. Part II is devoted to acceptance sampling. Part III covers the design of experiments, while Part IV discusses related fields. The twenty-three papers in this volume stem from The 11th International Workshop on Intelligent Statistical Quality Control, which was held in Sydney, Australia from August 20 to August 23, 2013. The event was hosted by Professor Ross Sparks, CSIRO Mathematics, Informatics and Statistics, North Ryde, Australia and was jointly organized by Professors S. Knoth, W. Schmid and Ross Sparks. The papers presented here were carefully selected and reviewed by the scientific program committee, before being revised and adapted for this volume