Quadratic deviation of penalized mean squares regression estimates

Abstract

Our aim in this work is to give a global test of hypothesis concerning the smoothing spline estimate of a regression function. For this, we prove a central limit theorem for integrated squares of such estimates. That leads to a test whose confidence sets are either continuous or discrete L 2-balls. We consider the case of nonperiodic splines and the periodic splines for which we get explicit expressions of the constants involved in such a test.