Abstract
Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index models. A new central limit theorem is established for a plug-in estimator of the unknown link function. Meanwhile, a considerable extension to a class of partially nonlinear single-index models is discussed in Section 4. Monte Carlo simulation verifies these theoretical results. An empirical study furnishes an application of the proposed estimation procedures in practice.
| Original language | English |
|---|---|
| Pages (from-to) | 425-453 |
| Number of pages | 29 |
| Journal | Annals of Statistics |
| Volume | 44 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 2016 |
Keywords
- A trio of convergence rates
- Dual convergence rates
- Integrated time series
- Orthogonal series expansion
- Partially linear single-index models
- Single-index models
Cite this
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Estimation for single-index and partially linear single-index integrated models. / Dong, Chaohua; Gao, Jiti; Tjostheim, Dag Bjarne.
In: Annals of Statistics, Vol. 44, No. 1, 01.02.2016, p. 425-453.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Estimation for single-index and partially linear single-index integrated models
AU - Dong, Chaohua
AU - Gao, Jiti
AU - Tjostheim, Dag Bjarne
PY - 2016/2/1
Y1 - 2016/2/1
N2 - Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index models. A new central limit theorem is established for a plug-in estimator of the unknown link function. Meanwhile, a considerable extension to a class of partially nonlinear single-index models is discussed in Section 4. Monte Carlo simulation verifies these theoretical results. An empirical study furnishes an application of the proposed estimation procedures in practice.
AB - Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index models. A new central limit theorem is established for a plug-in estimator of the unknown link function. Meanwhile, a considerable extension to a class of partially nonlinear single-index models is discussed in Section 4. Monte Carlo simulation verifies these theoretical results. An empirical study furnishes an application of the proposed estimation procedures in practice.
KW - A trio of convergence rates
KW - Dual convergence rates
KW - Integrated time series
KW - Orthogonal series expansion
KW - Partially linear single-index models
KW - Single-index models
UR - http://www.scopus.com/inward/record.url?scp=85013223212&partnerID=8YFLogxK
U2 - 10.1214/15-AOS1372
DO - 10.1214/15-AOS1372
M3 - Article
VL - 44
SP - 425
EP - 453
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
IS - 1
ER -