Mathematical Sciences: Bounded Influence, High Efficiency, High Breakdown Estimation and Testing Procedures

推理程序将开发的问题，在一个线性模型的子假设检验。这些程序的特点是：(i)局部稳定性，即它们的影响函数是有界的；（ii）全局稳定性，即它们的击穿点和击穿斜率是非零的；以及（iii）比现有的鲁棒程序提高了效率。基于比Krasker-Welsch更有效的估计器的测试程序将被开发和研究。测试程序将根据其几何性质进行表征，并探讨构建置信区间的可能性。

Inferential procedures will be developed for the problem of subhypothesis testing in a linear model. The procedures will be characterized by (i) local stability, i.e. their influence function will be bounded, (ii) global stability, i.e. their breakdown point and breakdown slopes will be nonzero, and (iii) improved efficiency over existing robust procedures. Testing procedures based on estimators that are more efficient than the Krasker-Welsch will be developed and investigated. The test procedures will be characterized according to their geometrical properties and the possibility of constructing confidence intervals will be explored.