Piecewise linear approximation methods with stochastic sampling sites

We study a generalization of the classical piecewise linear approximation methods with equally spaced breaks by considering the sampling sites as random variables. The new methods are motivated by the facts that real-world data collected from what are perceived to be equally spaced sites suffer from random errors due to measurement inaccuracies and other known or unknown factors. We establish error estimates and convergence results under practical assumptions about the distribution of the sampling sites.