Mathematical Sciences: Inference and Curve-Fitting in Generalizations of Isotonic Regression Models

通常，适用于数据的模型必须遵守某些约束条件，例如单调性或单调性。这项研究集中在当约束可以描述为单峰性、分段单调性或N-凸性时的统计建模。拟合函数将来自由凸锥、几个凸锥的并集或具有线性变化的锥体的交点定义的函数类。将编写计算算法，检查这些程序的统计方面，并开发假设检验。

Often models fitted to data must obey certain constraints such as monotonicity or monotonicity for individual segments. This research concentrates on statistical modelling when the constraints can be described as either unimodality, piecewise monotonicity, or N-convexity. Fitted functions will come from classes of functions defined by convex cones, unions of several convex cones or intersections of a cone with a linear variety. Computational algorithms will be written, statistical aspects of these procedures will be examined and hypothesis tests will be developed.