A-optimal experimental design for locally adaptive regression models

Complex regression dependencies can be constructed using nonparametric models or based on the developing concept of locally adaptive regression models (LAR models The proposed LAR models are not identifiable in their original form. This is due to the fact that for any value of the factor, the sum of the values of the indicator function is equal to 1. The same problem exists in the problem of estimating the parameters of variance analysis models, when the levels of factors are encoded by the values of pseudo-variables. The issue of identifying LAR models is considered. A procedure for reducing the model is introduced in the same way as it is done for variance analysis models. Active identification of such models involves conducting experiments on the object according to the constructed a priori plan. The case is considered when the area of definition of the operating factors is divided into 2 or 3 subareas. The degree of belonging of factors to a particular partition is determined through the indicator function, taking a value from 0 to 1. The criteria used in constructing experimental plans are related to the accuracy of the estimates of the model parameters, such as the A-optimality criterion. The problem of constructing A-optimal plans is solved. The single-factor LAR model is used as the model. In this case, the number of partitions was chosen as 2 and 3, and a local linear model and quadratic model were chosen as the local model. For the first time, the proposed A-optimal plans are compared with previously constructed D-optimal plans. It is noted that for the constructed A-optimal plans, the average dispersion of parameter estimates is significantly less than for D-optimal plans. The obtained optimal plans can be used to synthesize discrete optimal plans on their basis.