Estimation of index regression models using the least absolute deviations

In the regression modeling scheme, the key step is the model specification selection, i.e. the mathematical form of the relationship between variables. In this work, a new specification of regression models - index regression, is proposed, which is a generalization of the Leontief production function. It is noted that when constructing index regressions, along with statistical information, it is also necessary to attract expert information about the retrospective period, which classifies them as expert-statistical regression models. The task of estimating the unknown parameters of index regression using the least absolute deviations is reduced to the problem of partial-Boolean linear programming. Using Hald’s data, an example of constructing index regressions is considered.