Spline-backfitted kernel smoothing of nonlinear additive autoregression model

By Li Wang, Lijian Yang. 2006

158 citations recorded by the source corpus.

Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the “curse of dimensionality.” Under rather weak conditions, we propose spline-backfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very high-dimensional time series, and theoretically reliable so inference can be made on the component functions with confidence. Simulation experiments have provided strong evidence that corroborates the asymptotic theory.

Subfields: Artificial Intelligence, Statistics and Probability, Signal Processing

View Paper: https://www.semanticscholar.org/paper/8260f08a621818a3bd38f06c2058ac8b959d9a25

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Shujie Ma
2. Lijian Yang
3. Rong Liu
4. Li Wang
5. Jeffrey S. Racine
6. Qiongxia Song
7. Shan Yu
8. Chenhui Liu

In Statistics and Probability

1. Shujie Ma
2. Li Wang
3. Lijian Yang
4. Rong Liu
5. Jeffrey S. Racine
6. Guannan Wang
7. Qiongxia Song
8. Shan Yu

In Signal Processing

1. Shujie Ma
2. Lijian Yang
3. Rong Liu
4. Li Wang
5. Jeffrey S. Racine
6. Qiongxia Song

Citations in the corpus

• Oracally Efficient Two-Step Estimation of Generalized Additive Model (2013, unknown): “These results are established under substantially greater technical difficulty than existing works on additive model such as Wang and Yang (2007) tional complication is due to the lack of decomposition of spline 0.0 0.2 0.4 0.6 0.8 1.0 −0.2 −0.1 0.0 0.1 0.2”
• Estimation and Inference for Generalized Geoadditive Models (2020, methodology): “…spline method of Stone (1986), Xue and Liang (2010), and Wang et al. (2011); the kernel method of Yu, Park, and Mammen (2008), Yang, Sperlich, and Härdle (2003), and Liang et al. (2008); and the two-stage methods of Horowitz and Mammen (2004), Wang and Yang (2007), and Liu, Yang, and Härdle (2013).”
• Simultaneous variable selection and estimation in semiparametric modeling of longitudinal/clustered data (2013, methodology): “An anonymous referee pointed out the feasibility of obtaining the asymptotic “oracle” property of the nonparametric components in Ma and Yang [24].”
• Spline Regression in the Presence of Categorical Predictors (2015, methodology): “For applications of spline approaches, see Huang (1998) for functional ANOVA models, Huang and Yang (2004), Wang and Yang (2007) and Xue (2009) for additive models, Wang and Yang (2009) and Wang (2009) for single-index models, * Correspondence to: Jeffrey S. Racine, Department of Economics, Kenneth…”
• SPLINE ESTIMATION OF SINGLE-INDEX MODELS (2009, methodology): “The next lemma provides the exact form of Ŝ∗(θ−d), see Wang and Yang (2007b) for the proof.”
• Spline-backfitted kernel smoothing of partially linear additive model (2011, unknown): “Kernel procedures for PLAM, such as Fan and Li (2003) and Liang et al. (2008) satisfy criterion (iii) and partly (ii) but not (i) since they are computationally intensive when sample size n is large, as illustrated in the Monte-Carlo results of Xue and Yang (2006) and Wang and Yang (2007).”
• SPLINE-BACKFITTED KERNEL SMOOTHING OF ADDITIVE COEFFICIENT MODEL (2010, methodology): “For the additive model of Wang and Yang (2007), there is only one such unknown constant, and it is√ n-consistently estimated by the sample mean Y .”
• Varying Index Coefficient Models (2015, unknown): “…a knot sequence with N ≡ Nn interior knots, denoted by ξ1 = · · · = 0 = ξq < ξq+1 < · · · < ξq+N < 1 = ξN+q+1 = · · · = ξN+2q, where N increases along with the number of subjects n. Space Gn consists of functions, say , satisfying (i) is a polynomial of degree q − 1 on each of subintervals Is =…”