Nonparametric Approximation of the Density Function Logarithm of the Two-dimensional Random Variable

Consideration was given to a method for approximating the probability density of a two-dimensional random variable with separate stages of generating the local estimates and smoothing the random errors. It was proposed to decompose the space on the basis of the source data into minimal-size domains where the local estimates of the density logarithm which correspond to the observation model with additive errors accepted in the regression analysis were generated. The error covariance matrix was shown to be completely definite and independent of the original density, which made it possible to apply the apparatus of nonparametric regression to optimizing the choice of the smoothing parameter.