A Note on Nonparametric Regression with β-Mixing Sequences

Abstract

Statistical risks of least-squares estimates of a regression function (possibly nonlinear) are studied under a β-mixing setup. The assumptions are minimal and are virtually the same as those of the i.i.d. case. The bounds obtained are optimal, up to a term of order log n. Similar results are also obtained for complexity regularized regression estimates in the presence of penalty functions.

Keywords:

• Convergence rate
• Coupling
• Least-squares
• β-Mixing
• Nonparametric regression

Mathematics Subject Classification:

• Primary 62G07
• Secondary 62E20