To the problem of nonparametric robust estimation of the regression function on observations

There are parametric and nonparametric statistical models in the literature. These models differ from each other in levels of the prior indeterminacy in the statistical description of observations. The difference in ways these models were created tends to smoothing by introduction of transition models. It is explained by the fact that a statistical model, as well as any other model, is inevitable idealization and it can be only successful approximation of actual processes at its best. Emphasizing this fact, Box writes: “All models are irregular, but some of them are useful”. When using statistical procedures it is desirable to have information about what deviations have a decisive influ- ence on the final conclusion at statistical analysis. In case the true distribution is not normal, there can be questions of normal theory reference procedures applicability. The recent research approach called “robast statistics” and offered as “third generation statistics” after parametric and nonparametric statistics by American mathematician J. Tyyuki is devoted to answer formulated above questions and create statistical procedures insensitive to deviations from assump- tions. A number of publications on this approach constantly increases, there are already monographs, among them the first book of Hyubera, the book by F. Hampel and others, educational literature is also available. The “robust” term, which corresponds to the definition “rough, strong”, was introduced into statistical literature by Box in 1953 and since the middle of the sixtieth this term has became conventional for the section of statistics where statistical procedures insensitive to deviations from the accepted model assumptions develop. The robust idea has had a long history, which was described in Stigler’s work. It appears in the work of K. Gauss, S. Newcomb, A. Eddington and others. However systematic development of robust ideas began with J. Tyyuki’s works and, especially, after the work of Hyuber in 1964. In this work an estimation of functions with a data outlier problem is given. In case of nonparametric indeterminacy the following steps are used to solve the problem: 1) the type of regression function with input data is set; 2) function estimation is applied. We suggest the following reliable robust nonparametric estimation approach. The main idea is to exclude the data which can affect estimation.