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High dimensional generalized empirical likelihood for moment restrictions with dependent data

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  • Chang, Jinyuan
  • Chen, Song Xi
  • Chen, Xiaohong

Abstract

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment restrictions, as well as the degree of data dependence. It is shown that even in the high dimensional time series setting, the GEL ratio can still behave like a chi-square random variable asymptotically. A consistent test for the over-identification is proposed. A penalized GEL method is also provided for estimation under sparsity setting.

Suggested Citation

  • Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
  • Handle: RePEc:eee:econom:v:185:y:2015:i:1:p:283-304
    DOI: 10.1016/j.jeconom.2014.10.011
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    Cited by:

    1. Xiaohong Chen & Yin Jia Jeff Qiu, 2016. "Methods for Nonparametric and Semiparametric Regressions with Endogeneity: A Gentle Guide," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 259-290, October.
    2. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
    3. repec:eee:econom:v:208:y:2019:i:1:p:211-230 is not listed on IDEAS
    4. repec:eee:jmvana:v:171:y:2019:i:c:p:270-283 is not listed on IDEAS
    5. Qinqin Hu & Lu Lin, 2017. "Conditional sure independence screening by conditional marginal empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 63-96, February.
    6. Chaohua Dong & Jiti Gao & Bin Peng, 2018. "Series estimation for single-index models under constraints," Monash Econometrics and Business Statistics Working Papers 5/18, Monash University, Department of Econometrics and Business Statistics.
    7. repec:eee:econom:v:206:y:2018:i:1:p:57-82 is not listed on IDEAS
    8. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," LSE Research Online Documents on Economics 87513, London School of Economics and Political Science, LSE Library.
    9. repec:eee:ecolet:v:178:y:2019:i:c:p:1-4 is not listed on IDEAS
    10. repec:eee:econom:v:202:y:2018:i:1:p:57-74 is not listed on IDEAS
    11. Dou, Baojun & Parrella, Maria Lucia & Yao, Qiwei, 2016. "Generalized Yule–Walker estimation for spatio-temporal models with unknown diagonal coefficients," Journal of Econometrics, Elsevier, vol. 194(2), pages 369-382.
    12. repec:eee:jmvana:v:164:y:2018:i:c:p:22-39 is not listed on IDEAS
    13. Dou, Baojun & Parrella, Maria Lucia & Yao, Qiwei, 2016. "Generalized Yule–Walker estimation for spatio-temporal models with unknown diagonal coefficients," LSE Research Online Documents on Economics 67151, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    Generalized empirical likelihood; High dimensionality; Penalized likelihood; Variable selection; Over-identification test; Weak dependence;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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