Оценка параметров по засоренным выборкам

Abstract

Parametric estimates based on contaminated samples are considered in the paper. The paper provides an over-view of algorithms for estimating the mean and the variance for a one-dimensional sample, as well as estimating the mean vector and the covariance matrix for a multidimensional sample. The paper uses the Minimal Covariance Determinant (MCD) algorithm adapted for one-dimensional sample and the MCD algorithm for multidimensional sample. The parameters are estimated on a subsample, the size of which is determined by a given confidence probability. Examples for samples with different levels of contamination are considered. In both examples, the sample was a union of two subsamples. The first subsample, the main one, was generated by normal distribution laws. The second subsample, auxiliary, was generated by different distribution laws. The examples demonstrate the dependence of the estimation accuracy on the confidence level and contamination. The figures illustrate the operation of the MCD algorithm. The main idea of the paper is to show the robustness of the MCD algorithm.