Interval kernel regression

Kernel regression is more attractive when it is not possible to determine explicit parametric form of the model and moreover, it does not depend on probabilistic distribution. This paper introduces kernel regression in which the input data set is described by interval-value variables. Two model families are considered. The first family estimates the bounds of the intervals regarding either a smooth function for center variables of the intervals (first model) or two smooth functions for range and center variables, respectively (second model). The second family performs the estimates of the intervals based on regression mixtures. These mixtures assume either a smooth function for center variables and a linear function based on least squares for range variables (third model) or a smooth function for range variables and a linear function for center variables (fourth model). The predictions of the lower and upper bounds of new intervals are computed and two different simulation studies are carried out to validate these predictions. Five real-life interval data sets are also considered. The prediction quality is assessed by a mean magnitude of relative error calculated from a test data set.