NONPARAMETRIC ESTIMATION OF ADDITIVE NONLINEAR ARX TIME SERIES: LOCAL LINEAR FITTING AND PROJECTIONS

Near-Linear Time Local Polynomial Nonparametric Estimation

Local polynomial regression (Fan & Gijbels, 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this paper, we significantly accelerate the computation of local polynomial estimates ...

Nonparametric Estimation of Nonlinear Dynamics by Local Linear Approximation

This chapter discusses nonparametric estimation of nonlinear dynamical system models by a method of metric-based local linear approximation. By specifying a metric such as the standard metric or the square metric on the Euclidean space and a weighting function based on such as the exponential function or the cut-off function, it is possible to estimate values of an unknown vector field from exp...

Multivariate Regression Estimation : Local Polynomial Fitting for Time Series

We consider the estimation of the multivariate regression function m (x 1 , . . . ,xd) = E [ψ (Yd) | X 1 = x 1 , . . . ,Xd = xd], and its partial derivatives, for stationary random processes {Yi ,Xi} using local higher-order polynomial fitting. Particular cases of ψ yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is establi...

Nonlinear Time Series: Nonparametric and Parametric Methods

Boosting nonlinear additive autoregressive time series

Within the last years several methods for the analysis of nonlinear autoregressive time series have been proposed. As in linear autoregressive models main problems are model identification, estimation and prediction. A boosting method is proposed that performs model identification and estimation simultaneously within the framework of nonlinear autoregressive time series. The method allows to se...