On a Method of Two-Dimensional Smoothing

Regression analysis has the task of finding a functional relationship between the observed values the studied process. The raw data is the realization of a random variable, it is therefore considered dependent on the expectation. This problem can be solved by “smoothing” the raw data. Smoothing is the process of removing the noise and insignificant fragments while preserving the most important properties of the data structure. It is similar to finding the expectation of data. Data smoothing usually attained by parametric and nonparametric regression. The nonparametric regression requires a prior knowledge of the regression equation form. However, most of the investigated data cannot be parameterized simply. From this point of view, nonparametric and semiparametric regression represents the best approach to smoothing data. The aim of the research is development and implementation of the fast smoothing algorithm of two-dimensional data. To achieve this aim previous works in this area have been analyzed and its own approach has been developed,improving the previous ones. As a result, this paper presents the algorithm that quickly and with minimal memory consumption cleanses the data from the “noise” and “insignificant” parts. To confirm the “efficiency” of the algorithm the comparisons with other generally accepted approaches were carried out on simulated and real data with other generally accepted approaches. The results of these comparisons are also shown in the paper.

nonparametric regression, two-dimensional estimation, penalized splines, smoothing splines, cross-validation, discrete cosine transform