Nonparametric Control Charts Based on Data Depth for Location Parameter
- 27 Downloads
Traditional control charts like Hotelling \(T^2\) are based on the assumption of multivariate normality and also inapplicable to high-dimensional data. A notion of data depth has been used to measure centrality of a given point in a given data cloud. The data depth inferences do not require multivariate normality and any constraint on the dimension of the data. Liu (J Am Stat Assoc 90(432):1380–1387, 1995) provided control charts for a multivariate processes based on data depth, and the performance of the chart is not reported. There exist few tests for the location parameter of multivariate distribution based on data depth. Using these tests, we proposed nonparametric control charts to detect a shift in the location parameter of the multivariate process. We investigate the performance of the proposed control charts using the average run-length measure for various distributions. Also, the control chart procedure is illustrated by using wine quality data.
KeywordsMultivariate processes Depth functions DD plot Bootstrapping
Both the authors would like to acknowledge the financial support received from University Grants Commission under Major Research Project (F. No. 43-542/2014 (SR)) to carry out the research work. The second author also would like to thank Department of Science and Technology (DST), Science and Engineering Research Board (SERB), New Delhi, for providing financial support under Extra Mural Research scheme [EMR/2017/167] to carry out the research work.
- 7.Hotelling H (1947) Multivariate quality control. In: Techniques of statistical analysis. McGraw-Hill, New YorkGoogle Scholar
- 21.Tukey JW (1975) Mathematics and the picturing of data. In: Proceedings of the international congress of mathematicians, vol 2. Vancouver, pp 523–531Google Scholar