Nonparametric Estimation of the Quadratic Functional of a Multimodal Probability Density

Аннотация

A nonparametric method for estimating the mean square functional of a multimodal probability density of a one-dimensional random variable is examined. The proposed method is based on using the Sturgis and Heinhold–Gaede formulas and an optimum sampling procedure for sampling a range of values of random quantities. This method is compared with the traditional approach based on choosing a spread coefficient using the condition for the maximum of the likelihood function. The conditions for competence of this method are determined.