It is known that the fitted regression function based on conventional local smoothing procedures is not statistically consistent at jump positions of the true regression function. In this article, a curve-fitting procedure based on local piecewise-linear kernel estimation is suggested. In a neighborhood of a given point, a piecewise-linear function with a possible jump at the given point is fit...

Transition points are common in physiological processes. However the 28 transition between normothermia and hypothermia during haemorrhagic shock has 29 rarely been systematically quantified from intensive time series data. We estimated the 30 critical transition point (CTP) and provided confidence intervals for core body 31 temperature response to acute severe haemorrhage in a conscious rat mo...

The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switching laws. The paper derives generalization error bounds in these two settings...

We propose a novel general piecewise surface regression model that allows for arbitrary functions to be used in each piece, and arbitrary boundary surfaces between pieces. We also give an EM-based algorithm for this model, EMPRR, that scales to high dimensions. We compare EMPRR's performance with those of model trees and functional trees, two regression tree learning methods, on synthetic piece...

Simple linear regression tries to determine a linear relationship between a given variable X (predictor) and a dependent variable Y. Since most of the environmental problems involve complex relationships, X-Y relationship is often better modeled through a regression where, instead of fitting a single straight line to the data, the algorithm allows the fitting to bend. Piecewise regressions just...

In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investigate the existence, uniqueness and convergence of approximate solutions. Finally the accuracy of piecewise approximate method b...

We review and expand somewhat on some recent developments concerning the construction and analysis of piecewise polynomial estimators for the regression problem in Mathematical Learning Theory. The discussion will center on two issues. The first of these is computational efficiency including possible online capability. The second is universality by which we mean the capability of the estimator ...

We consider the regression problem and describe an algorithm approximating the regression function by estimators piecewise constant on the elements of an adaptive partition. The partitions are iteratively constructed by suitable random merges and splits, using cuts of arbitrary geometry. We give a risk bound under the assumption that a “weak learning hypothesis” holds, and characterize this hyp...

Research in the field of nonparametric shape constrained regression has been extensive and there is need for such methods in various application areas, since shape constraints can reflect prior knowledge about the underlying relationship. It is, for example, often natural that some intensity first increases and then decreases over time, which can be described by a unimodal shape constraint. But...

PURPOSE The objective of this study was to compare multiple methods for estimation of PWV from 4D flow MRI velocity data and to investigate if 4D flow MRI-based PWV estimation with piecewise linear regression modeling of travel-distance vs. travel time is sufficient to discern age-related regional differences in PWV. METHODS 4D flow MRI velocity data were acquired in 8 young and 8 older (age:...