Minimum complexity regression estimation with weakly dependent observations

Given N strongly mixing observations.

[1]  C. Craig.  On the Tchebychef Inequality of Bernstein , 1933 .

[2]  M. Rosenblatt.  A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Y. Davydov.  Mixing Conditions for Markov Chains , 1974 .

[4]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[5]  C. Withers.  Conditions for linear processes to be strong-mixing , 1981 .

[6]  P. Robinson.  NONPARAMETRIC ESTIMATORS FOR TIME SERIES , 1983 .

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

[8]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[9]  G. Roussas.  Nonparametric regression estimation under mixing conditions , 1990 .

[10]  Halbert White,et al.  Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings , 1990, Neural Networks.

[11]  A. Barron.  Approximation and Estimation Bounds for Artificial Neural Networks , 1991, COLT '91.

[12]  András Faragó,et al.  Strong universal consistency of neural network classifiers , 1993, IEEE Trans. Inf. Theory.

[13]  E. Masry.  Strong consistency and rates for deconvolution of multivariate densities of stationary processes , 1993 .

[14]  Kurt Hornik,et al.  Degree of Approximation Results for Feedforward Networks Approximating Unknown Mappings and Their Derivatives , 1994, Neural Computation.

[15]  Daniel F. McCaffrey,et al.  Convergence rates for single hidden layer feedforward networks , 1994, Neural Networks.

[16]  M. A. Arcones,et al.  Central limit theorems for empirical andU-processes of stationary mixing sequences , 1994 .

[17]  Bin Yu.  RATES OF CONVERGENCE FOR EMPIRICAL PROCESSES OF STATIONARY MIXING SEQUENCES , 1994 .

[18]  D. Pollard,et al.  An introduction to functional central limit theorems for dependent stochastic processes , 1994 .

[19]  Gábor Lugosi,et al.  Nonparametric estimation via empirical risk minimization , 1995, IEEE Trans. Inf. Theory.

[20]  P. Massart,et al.  Invariance principles for absolutely regular empirical processes , 1995 .