论文信息 - A Note on Nonparametric Regression with β-Mixing Sequences

A Note on Nonparametric Regression with β-Mixing Sequences

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.

Majid Mojirsheibani | M. Mojirsheibani | Qunshu Ren | Qunshu Ren

[1] M. Kohler. Inequalities for uniform deviations of averages from expectations with applications to nonparametric regression , 2000 .

[2] R. Syski,et al. Random Walks With Stationary Increments and Renewal Theory , 1982 .

[3] Y. Baraud,et al. ADAPTIVE ESTIMATION IN AUTOREGRESSION OR β-MIXING REGRESSION VIA MODEL SELECTION By , 2001 .

[4] Adam Krzyzak,et al. A Distribution-Free Theory of Nonparametric Regression , 2002, Springer series in statistics.

[5] D. Pollard. Convergence of stochastic processes , 1984 .

[6] Dharmendra S. Modha,et al. Minimum complexity regression estimation with weakly dependent observations , 1996, IEEE Trans. Inf. Theory.

[7] David L. Neuhoff,et al. Asymptotic distribution of the errors in scalar and vector quantizers , 1996, IEEE Trans. Inf. Theory.

[8] Peter L. Bartlett,et al. Efficient agnostic learning of neural networks with bounded fan-in , 1996, IEEE Trans. Inf. Theory.

[9] Denis Bosq,et al. Nonparametric statistics for stochastic processes , 1996 .