Construction of robust estimates of meano values and variations of two-dimensional data on the basis of the spectral matrix norm
The problem of estimating of mean values and variations of two-dimensional data is considered. Data can be represented as a matrix in discrete case, or as a function of two variables in the continuous case. Estimate of the mean value of discrete data is found as solution of the optimization problem with objective function in the form of the spectral norm of a matrix. In the continuous case the problem is reduced to the discrete case by sampling the domain of function. The inequalities to assess the influencet of errors in the data matrix on the results of calculations of mean values and variations in data are derived. The results of test calculations confirm the robustness of the estimates of the mean values and variations derived from spectral norms with respect to data errors.