Sieve extremum estimates for weakly dependent data

Many non/semiparametric time series estimates may be regarded as different forms of sieve extremum estimates. For stationary absolute regular mixing observations, the authors obtain convergence rates of sieve extremurn estimates and root-n asymptotic normality of 'plug-in' sieve extremum estimates of smooth functionals. As applications to time series models, they give convergence rates for nonparametric ARX(p,q) regression via neural networks, splines, wavelets; root-n asymptotic normality for partial linear additive AR(p) models, and monotone transformation AR(1) models.

[1]  D. Andrews.  Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models , 1991 .

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

[3]  W. Wong,et al.  Convergence Rate of Sieve Estimates , 1994 .

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

[5]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

[6]  C. J. Stone,et al.  Optimal Global Rates of Convergence for Nonparametric Regression , 1982 .

[7]  Ryozo Yokoyama.  Moment bounds for stationary mixing sequences , 1980 .

[8]  I. Johnstone,et al.  Wavelet Shrinkage: Asymptopia? , 1995 .

[9]  W. Wong,et al.  On Maximum Likelihood Estimation in Infinite-Dimensional Parameter Spaces , 1991 .

[10]  A. Ronald Gallant,et al.  Convergence Rates of SNP Density Estimators , 1996 .

[11]  L. Goddard.  Approximation of Functions , 1965, Nature.

[12]  R. D. Vore.  Monotone Approximation by Splines , 1977 .

[13]  S. Geman,et al.  Nonparametric Maximum Likelihood Estimation by the Method of Sieves , 1982 .

[14]  Y. Makovoz.  Random Approximants and Neural Networks , 1996 .

[15]  P. Robinson.  ROOT-N-CONSISTENT SEMIPARAMETRIC REGRESSION , 1988 .

[16]  Xiaotong Shen,et al.  On methods of sieves and penalization , 1997 .

[17]  P. Massart,et al.  Rates of convergence for minimum contrast estimators , 1993 .

[18]  P. Robinson,et al.  Best nonlinear three-stage least squares estimation of certain econometric models , 1991 .

[19]  H. Ichimura,et al.  SEMIPARAMETRIC LEAST SQUARES (SLS) AND WEIGHTED SLS ESTIMATION OF SINGLE-INDEX MODELS , 1993 .

[20]  E. Eberlein.  Weak convergence of partial sums of absolutely regular sequences , 1984 .

[21]  Peter E. Rossi,et al.  Nonlinear dynamic structures , 1993 .

[22]  S. Meyn,et al.  Stability of Markovian processes I: criteria for discrete-time Chains , 1992, Advances in Applied Probability.

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

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