Maximum compatibility method for data fitting under interval uncertainty

For the linear regression model, the data-fitting problem under the interval uncertainty of the data is studied. As an estimate of the linear function parameters, it is proposed to take their values that deliver the maximum for the so-called recognizing functional of the parameter set compatible with the data (the maximum compatibility method). The properties of the recognizing functional, its interpretation, and the properties of the estimates obtained using the maximum compatibility method are investigated. The relationships to other data analysis methods are discussed, and a practical electrochemistry problem is solved.