Non-Parametric Estimation of a Single Inflection Point in Noisy Observed Signal

Detection of abrupt changes, including inflection points, in the observed noisy signals is an important and challenging problem in engineering and science. Several methods have been proposed to solve this problem and proved to be successful for specific applications. Yet, there is demand for new and general approaches that are applicable to broader range of applications. The change point detection problem can be divided into two categories; i) sequential or on-line, and ii) batch or off-line. In on-line methods, the observed data are inspected sequentially to catch a change as soon as it occurs. These methods are mainly used in quality control, real time surveillance & vision systems, and real time fault detection in computer networks [1-6]. In offline methods the entire data set is observed and can be processed at once. The off-line problems are growing fast and have attracted many researchers in computational biology and biostatistics as well as offline computer vision applications [7-14]. In previous work [15,16], often Cross Validation (CV) is used to select the bandwidth to locate the discontinuities in the observed signal including inflection points, change points, jumps and valleys. Discontinuities in [15], assuming an unknown number, are located by detecting the zero crossing of the second derivative and the local maxima of the first derivative while CV is used to estimate bandwidth parameters. Bootstrap is used in [16] for designing a nested CV method for detecting the change points by finding the local maxima of the first derivative while considering the number of change points is unknown.