Oracally efficient estimation of autoregressive error distribution with simultaneous confidence band

Oracally efficient spline smoothing of nonlinear additive autoregression models with simultaneous confidence band

Under weak conditions of smoothness and mixing, we propose splinebackfitted spline (SBS) estimators of the component functions for nonlinear additive autoregression model. The proposed SBS estimator is both computationally expedient for analyzing high dimensional large time series data since it can circumvent the curse of dimensionality, and theoretically reliable as the estimator is oracally e...

Experiments with autoregressive error estimation

Estimation in autoregressive model with measurement error

Consider an autoregressive model with measurement error: we observe Zi = Xi + εi, where Xi is a stationary solution of the autoregressive equation Xi = fθ0(Xi−1) + ξi. The regression function fθ0 is known up to a finite dimensional parameter θ. The distributions of X0 and ξ1 are unknown whereas the distribution of ε0 is completely known. We want to estimate the parameter θ by using the observat...

Oracally Efficient Two-Step Estimation of Generalized Additive Model

Oracally Efficient Two-Step Estimation of Generalized Additive Model Rong Liu a b , Lijian Yang a c & Wolfgang K. Härdle d a Center for Advanced Statistics and Econometrics Research , Soochow University , China b Department of Mathematics and Statistics , University of Toledo , Toledo , OH , 43606 c Department of Statistics and Probability , Michigan State University , East Lansing , MI , 48824...

Neural Autoregressive Distribution Estimation

We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density esitmation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discu...