Abstract

This paper introduces a class of nonparametric two-sample semi-sequential tests for multivariate and high-dimensional data using distance metrics. This paper aims to provide a class of robust tests for the online detection of a shift in a multivariate data stream in Phase II with few training samples. The Euclidean distances of data points from the origin and the notion of Euclidean interpoint distance are used along with the partially sequential sampling scheme. The statistical methodologies are discussed in detail. Some asymptotic results are derived, and some numerical results based on Monte Carlo are also presented to justify the usefulness of the large sample results in practice. The power performances of the proposed test against some fixed alternatives are obtained computationally. An illustration of the proposed procedure is presented with real data related to the quality inspection of semiconductor chips. Some concluding remarks are offered, along with some possible future research directions.