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

通常，拟合数据的模型必须遵守某些约束 例如单个段的单调性或单调性。 这项研究集中在统计建模时， 约束可以被描述为单峰、分段 单调性或N-凸性。 拟合函数将来自 由凸锥定义的函数类，多个函数的并集 凸圆锥或圆锥与线性变量的交点。 将编写计算算法、统计方面的 这些程序将被检查，假设检验将被 开发

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.