DIVERSITY OF THE MODELS FOR REGRESSION ANALYSIS (generalizing article)

Streamlining the results of scientific research entails the necessity of the uniform understanding of terminology, accumulation of facts and insight of the development trend. We consider those issues on the example of «regression analysis model (recovery of the dependencies)» to form a unified methodological base for discussing various particular issues in this field. Four methods are considered. The models of the method of least squares with deterministic independent variable are singled out. According to the new paradigm of applied statistics, the distribution of deviations (errors, discrepancies) should be considered arbitrary, with one restriction, to obtain the limiting distributions of the estimates of parameters and dependencies, it is expedient to assume the fulfillment of conditions of the central limit theorem. The second basic type of probabilistic-statistical models of the method of least squares is based on a sample of random vectors. The dependence is nonparametric and distribution of the two-dimensional vector is arbitrary. Estimate of the variance of the independent variable can be considered only in a model based on a sample of random vectors, as well as the coefficient of determination as a criterion for the quality of the model. The issues of smoothing time series are discussed. Methods of reconstructing dependencies in spaces of general nature are considered. It is shown that the limiting distribution of the natural estimate of the dimensionality of the model is geometric, and construction of the informative subset of features comes across the effect of «inflation of the correlation coefficients». Different approaches to the regression analysis of interval data are discussed: the approach of confluent analysis becomes a thing of the past. An analysis of the variety of models of regression analysis leads to the conclusion that there is no single «standard model». Critical analysis of the hardened beliefs is necessary for competent development and application of mathematical methods of research, in particular, for transition to a modern paradigm of applied statistics.

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