NONPARAMETRIC METHOD OF RECONSTRUCTING PROBABILITY DENSITY ACCORDING TO THE OBSERVATIONS OF A RANDOM VARIABLE

Abstract

When investigating the statistical characteristics of a field formed by locally inhomogeneous regions, the problem of reconstructing the probability density function with several vertices on the basis of the results of experimental observations arises. In this case, it is very difficult to apply parametric methods for reconstructing the probability density. Therefore, to restore the probability density, it makes sense to use non-parametric methods of recovery. The Rosenblatt-Parzen method usually used for these purposes has low accuracy and convergence rate. The method proposed in the work of Chentsov N.N. has higher accuracy and convergence rate. However, for multi-vertex distributions its convergence rate is also low. Similar conclusions can be drawn regarding the method proposed in the work of Vapnik V.N. Thus, the problem of developing a technique for reconstructing the multi-vertex probability density on the basis of the results of experimental observations becomes very urgent. The article suggests a nonparametric method of reconstructing probability density according to the observations of a random variable. The method is regular in the sense of Tikhonov regularization and, as the analysis and solution of test problems show, it has sufficiently high accuracy and convergence rate.

Keywords

• nonparametric methods
• distribution function
• probability density
• sampling function
• whittaker series
• quasisolution