Average quadratic error of the estimate of the first order splines in the model of linear regression - Petunina , M. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 1991)
We study the mean quadratic error of an estimate of splines of the first order, which is obtained by the method of least squares under the assumption that the data represents a superposition of proper values of a spline and a white noise. A quantitative formula for the quadratic mean error is found and its asymptotics is investigated.