Robust construction of regression models based on the generalized least absolute deviations method

Systems monitoring based on robust estimation of stochastic time series models

“…One of the methods for estimating model parameters (1) under conditions of stochastic data heterogeneity is the robust estimation method (REM), based on minimizing the convex-concave loss function. As loss functions here we use functions of the form [4][5][6]: (5)…”

“…They must either be set on the basis of a priori information or evaluated in some way. Note that the advantage of asymptotically bounded loss functions of the form (3) or (4) over (5) is that the estimates of the model parameters (1) obtained on their basis have a smaller bias for asymmetric contaminations.…”

“…In this regard, standard algorithms for finding a minimum solution cannot be used to find a solution. The presence of several minima of the objective function suggests an analogy with the generalized least absolute deviations method [5], but unlike the latter, the REM solution is not located at the nodal points. However, nodal points are already present in a sufficiently small neighborhood of the solution.…”

“…The found solutions of system (11) must be investigated in order to determine which of them is the minimum point, which in turn requires the calculation of the second derivatives of function (8) and the determination of the sign of the determinant of the Hess matrix. Consider an algorithm for finding the minimum for a concave loss function [5]. Let's check its work for the objective function (6) , and the minimum of the function is at the point…”

Forecasting and Analysis Tools for Regional Industries’ Dynamics

“…However, it is very sensitive to outliers presented in heavy-tailed distributions. The least absolute deviations method is seen as more reliable [7]:…”