About specialities of numerical estimation of smoothing parameter of probability density functions of random sequences in Parzen-Rosenblatt approximation
Sergey V. Porshnev, A.S. Koposov · Journal of Physics Conference Series · 2018
The methods of nonparametric statistics are very useful in data analysis. One of the most popular methods is called Parzen-Rosenblatt approximation. This method turns out to be effective, for example, in a problem of estimation of longevity of pipelines or in the analysis of the statistical characteristics of traffic flows. This paper discusses the recommendations for application of a method, which was performed by Parzen and Rosenblatt, in a problem of recovering a probability density function from a sample of random data with a bounded scattering region. It was shown that there are some difficulties during calculation of information functional. This paper gives an explanation of causes which lead to a nonmonotonicity of an information functional and which are based on a finite precision of computer calculations. It was proved a choice of initial value of smoothing parameter for different kernel types and was proposed an algorithm for finding a maximal value of information functional.