Empirical Likelihood for Partially Linear Models
By Jian Qing Shi, T. Lau. 2000
163 citations recorded by the source corpus.
In this paper, we consider the application of the empirical likelihood method to partially linear model. Unlike the usual cases, we first propose an approximation to the residual of the model to deal with the nonparametric part so that Owen's (1990) empirical likelihood approach can be applied. Then, under quite general conditions, we prove that the empirical log-likelihood ratio statistic is asymptotically chi-squared distributed. Therefore, the empirical likelihood confidence regions can be constructed accordingly.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/42bad7a1ffff21b51748105df100a927c2f209c3
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
- Liugen Xue
- Lixing Zhu
- I. Van Keilegom
- Songxi Chen
- Heng Lian
- Olivier Scaillet
- Maria Pacurar
- Tommaso Cai
In Statistics and Probability
- Liugen Xue
- I. Van Keilegom
- Heng Lian
- Lixing Zhu
- Songxi Chen
- Wenceslao González-Manteiga
- Tommaso Cai
- Rosa M. Crujeiras
Citations in the corpus
- Empirical likelihood confidence intervals for nonparametric functional data analysis (2009, background): “the Appendix hold, and ||βˆ−β 0|| = Op(n−1/2), then lre ∗ n(r(x 0)) = −2logLRg ∗ n(r(x 0)) → χ2 1 in distribution. Most previous studies on empirical likelihood inference for partially linear models (Shi and Lau, 2000; Lu, 2009; Chen and Cui, 2008) focused on constructing confi- dence regions for the”
- Empirical likelihood confidence regions in a partially linear single‐index model (2006, background): “Wang and Jing (1999) and Shi and Lau (2000) considered a partial linear model with fixed design: see also Chen and Qin (1993), DiCiccio et al. (1991), Kitamura (1997), Qin (1993), Qin and Lawless (1994) and Zhang (1997).”
- A review on empirical likelihood methods for regression (2009, methodology): “It goes back to Thomas and Grunkemeier (1975), who proposed a method for constructing confidence intervals for survival probabilities when the data are subject to random right censoring, which directly motivates Owen’s invention of the EL as recalled in Owen (2001).”