Penalized generalized empirical likelihood with a diverging number of general estimating equations for censored data

2020 ◽  
Vol 48 (1) ◽  
pp. 607-627
Author(s):  
Niansheng Tang ◽  
Xiaodong Yan ◽  
Xingqiu Zhao
Keyword(s):  
Censored Data ◽  
Empirical Likelihood ◽  
Estimating Equations ◽  
Generalized Empirical Likelihood

Generalized empirical likelihood non-nested tests

2002 ◽  
Vol 107 (1-2) ◽  
pp. 99-125 ◽  
Author(s):  
Joaquim J.S. Ramalho ◽  
Richard J. Smith
Keyword(s):  
Empirical Likelihood ◽  
Generalized Empirical Likelihood

EFFICIENT TWO-STEP GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION AND TESTS WITH MARTINGALE DIFFERENCES

2020 ◽  
pp. 1-40 ◽  
Author(s):  
Fei Jin ◽  
Lung-fei Lee
Keyword(s):  
Empirical Likelihood ◽  
Generalized Method Of Moments ◽  
Likelihood Estimation ◽  
Nuisance Parameters ◽  
Martingale Differences ◽  
Generalized Empirical Likelihood ◽  
Moment Functions ◽  
The Impact ◽  
Bias Terms ◽  
Parameters Of Interest

This paper considers two-step generalized empirical likelihood (GEL) estimation and tests with martingale differences when there is a computationally simple $\sqrt n-$ consistent estimator of nuisance parameters or the nuisance parameters can be eliminated with an estimating function of parameters of interest. As an initial estimate might have asymptotic impact on final estimates, we propose general C(α)-type transformed moments to eliminate the impact, and use them in the GEL framework to construct estimation and tests robust to initial estimates. This two-step approach can save computational burden as the numbers of moments and parameters are reduced. A properly constructed two-step GEL (TGEL) estimator of parameters of interest is asymptotically as efficient as the corresponding joint GEL estimator. TGEL removes several higher-order bias terms of a corresponding two-step generalized method of moments. Our moment functions at the true parameters are martingales, thus they cover some spatial and time series models. We investigate tests for parameter restrictions in the TGEL framework, which are locally as powerful as those in the joint GEL framework when the two-step estimator is efficient.

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