Eliminating user-interaction in probability density estimation

Abstract

Despite the extensive literature, describing the probability content of measurements remains an important topic for engineering problems. The histogram remains the golden standard, even though kernel density estimation is a strong competitor when smooth estimates are desired. Critical user interaction is required for the use of both the histograms and kernel densities. A good choice for the bandwidth is essential in both cases. On top of that the kernel density method requires a proper choice of the kernel. Incorrect choices may lead to incorrect results generated by either masking important details or introducing false details. In this paper, we propose a new approach which requires no user-defined choices. The method is therefore fully automatic and provides the user a smooth density estimate of the probability content.