TITLE: A nonparametric on-line quality control procedure for vectorial observations
SPEAKER: David McDonald
The goal of an on-line quality control procedure is to rapidly detect an out-of-control situation; i.e., to detect a change in the sampling distribution after a change point. We first review a nonparametric Cusum procedure based on the sequential ranks for univariate data.
Many attempts have been made to assign sequential ranks to multivariate data. For instance ranks based on the Tukey depth have been used but the computations are prohibitive in high dimension. Instead we will score observations based on where they fall relative to previous observations.
Each successive observation creates a Voronoi cell indexed by the observation number. Suppose observation $n+1$ falls into the Voronoi cell with index $i$ where $i$ ranges from $1$ to $n$. Then observation $n+1$ has associated score $i/(n+1)$ and becomes the center of a new Voronoi cell with index $n+1$.
Before the change point, the scores are uniformly distributed. After the change point, the scores tend to be large since the observations tend to clump together. We use these scores in a Cusum procedure. We find we can approximately predict the on-target average run length of our procedure, and we get reasonable off-target run lengths for any kind of structural break like a change of mean or a change of dispersion.
David Mcdonald is a Professor in the Department of Mathematics at the University of Ottawa. He received his Ph.D. from U. de Montreal, and a Masters from King's College (London). He has held several visiting positions, including a stay at the Georgia Institute of Technology and Ecole Normale Superieure. He is also a Fellow of the Institute of Mathematical Statistics.