DescriptionThe concept of Scale Curve provides a graphical tool for analysis of multivariate data, with a broad range of statistical applications. Recent research in variants of Scale Curves have shown great promise, as they can be easily adapted to build robust non-parametric testing procedures under various scenarios, while preserving good power, and retaining the crucial virtues of easy computation and simple graphical representation.
This thesis investigates the properties of one such variant of Scale Curves, named the Determinant Scale Curve (dsc). It is shown that the dsc can be used to devise non-parametric exact tests for location of multivariate data with a special property (stated in next paragraph), under both one sample and multi-sample setups. Similar ideas are extended to tackle problems in linear regression, where the dsc is used to build tests for significance of the slope parameter.
For all the problems discussed, the dsc's actually provide a whole spectrum of tests. The tests at the rightmost end of the spectrum are shown to be Pitman equivalent to the benchmark most powerful tests for the given problem. As one moves towards the other end, the corresponding tests become progressively more and more robust, i.e. insensitive to outliers. Simulation results show that this robustification does not come with a serious loss of power under most situations.