How very simple digital signal processing techniques, such as numerical filtering and linear interpolation, may provide PDF estimates with improved statistical properties over the histogram and close to, or better than, what can be obtained using Kernel based estimators

P. Carbone, D. Petri and K. Barbé, “Nonparametric Probability Density Estimation via Interpolation Filtering,” in IEEE Transactions on Instrumentation and Measurement, vol. 66, no. 4, pp. 681-690, April 2017.DOI: 10.1109/TIM.2017.2657398.

In this paper, we discuss nonparametric estimation of the probability density function (PDF) of a univariate random variable. This problem has been the subject of a vast amount of scientific literature in many domains, while statisticians are mainly interested in the analysis of the properties of proposed estimators, and engineers treat the histogram as a ready-to-use tool for a data set analysis. By considering histogram data as a numerical sequence, a simple approach for PDF estimation is presented in this paper. It is based on basic notions related to the reconstruction of a continuous-time signal from a sequence of samples. When estimating continuous PDFs, it is shown that the proposed approach is as accurate as kernel-based estimators, widely adopted in the statistical literature. Conversely, it can provide better accuracy when the PDF to be estimated exhibits a discontinuous behavior. The main statistical properties of the proposed estimators are derived and then verified by simulations related to the common cases of normal and uniform density functions. The obtained results are also used to derive optimal, i.e., minimum integral of the mean square error, estimators.

Comments are closed.

Post Navigation