Statistical processing of a small sample of raw data using artificial orthogonalisation technology

Abstract

This paper addresses the task to devise a statistical estimation procedure in an event where the volume of the array of initial data used in processing is insufficient to correctly determine the parameters of the response function. The object of research is the technology of statistical processing of a small sample of data. The subject of the study is the methods of statistical estimation under conditions of a small sample of initial data. The main direction is to devise a special procedure for statistical processing of a small sample of initial data, which provides a correct statistical estimation of the parameters of the response function. The method for solving the problem is the selection of the most representative orthogonal replica-like subplan from the plan of a complete factorial experiment obtained by artificially orthogonalizing the results of a passive experiment. The necessity and expediency of the proposed procedure is a consequence of the unpredictability and uneven distribution of points in the phase space of coordinates. The result of the implementation of the corresponding procedure is a truncated orthogonal plan of the full factorial experiment, which provides the possibility of independent estimation of all coefficients of the regression polynomial describing the response function. Under conditions of a severe shortage of the number of measurements, the procedure makes it possible to isolate a representative orthogonal replica from the resulting plan of a complete factorial experiment. Using this subplan of the full factorial experiment plan makes it possible to evaluate all the coefficients of the regression polynomial that describes the desired response function. The corresponding computational procedure is based on solving the triaxial Boolean assignment problem