Multivariate isotonic regression and its algorithms
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Hoffmann, Linda and Xiaomi Hu(2009) . Multivariate Isotonic Regression and Its Algorithms. In Proceedings: 5th Annual Symposium: Graduate Research and Scholarly Projects. Wichita, KS: Wichita State University, p. 38-39
We use regression functions, which are the means of random variables, to interpret statistical inference. Often an order is imposed on the values of the regression function. Thus, we refer to the regression as an order restricted regression or an isotonic regression. In this paper we explain how to calculate multivariate isotonic regression. However, we investigate the case for a particular restriction on our elements. We impose relations between elements of the same row but not between rows. The technique is to decompose our multivariate model into univariate models so that prior knowledge about the simpler case can be used. Finally, we propose an algorithm to calculate multivariate isotonic regression. This algorithm could then be converted into a computer program.
Paper presented to the 5th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held at the Hughes Metropolitan Complex, Wichita State University, May 1, 2009.
Research completed at the Department of Mathematics & Statistics, College of Liberal Arts & Sciences