Choice of the regression model order

For a function to be obtained from its measurements containing a random error an approximation is sought as a stretch of a series in the system of functions. The most important step is finding the number of terms in this expansion. The approximation performance is estimated as the r. m. s. prediction error over the entire stretch or a specified system of points. Accurate and asymptotic expressions are obtained for the r. m. s. error with various assumptions. Criteria for choosing the model order on different kinds of prior information and numerical examples are provided.