Optimal level sets for bivariate density representation
For the bivariate density representation, there are a lot of results on level set estimation when the levels are fixed. The choice of levels is an important practical question and its answer requires both the definition of an optimal level and the construction of the method for finding it. Two scenarios of this problem are considered. The first one corresponds to a situation in which one has just a single density function to be represented. At the same time, the need arises to develop a joint representation for a lot of densities, and this is the second scenario of the paper. When the number of bivariate density functions to be represented is large, and when each density is recorded at a different time, a convenient way to represent them is using an animated graph, in which each image corresponds to the graph of each bivariate density. In this case each density by a few density level sets can be represented. Two approaches for quantifying the quality of a level set are developed. The first one uses distances between level sets and the second one is based on distances between density functions. In the paper, the consistency for the estimated levels is provided, and wide Monte Carlo simulated experiments illustrating the feasibility of the proposed method are presented.
graphical representation of bivariate densities
optimal representation of densities by level sets
scientific article; zbMATH DE number 6480454
scientific article