Empirical likelihood estimation and inference

2000 ◽  
pp. 119-150 ◽  
Author(s):  
Richard J. Smith
Keyword(s):  
Empirical Likelihood ◽  
Likelihood Estimation

scholarly journals Population empirical likelihood estimation in dual frame surveys

2020 ◽  
Author(s):  
Maria del Mar Rueda ◽  
Maria Giovanna Ranalli ◽  
Antonio Arcos ◽  
David Molina
Keyword(s):  
Empirical Likelihood ◽  
Likelihood Estimation ◽  
Dual Frame

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.

scholarly journals A NOTE ON GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATION OF SEMIPARAMETRIC CONDITIONAL MOMENT RESTRICTION MODELS

2016 ◽  
Vol 33 (5) ◽  
pp. 1242-1258 ◽  
Author(s):  
Naoya Sueishi
Keyword(s):  
Empirical Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Unknown Parameters ◽  
Conditional Moment ◽  
Finite Dimensional ◽  
Dimensional Parameters ◽  
Image Position ◽  
Asymptotically Efficient ◽  
Moment Restriction

This paper proposes an empirical likelihood-based estimation method for semiparametric conditional moment restriction models, which contain finite dimensional unknown parameters and unknown functions. We extend the results of Donald, Imbens, and Newey (2003, Journal of Econometrics 117, 55–93) by allowing unknown functions to be included in the conditional moment restrictions. We approximate unknown functions by a sieve method and estimate the finite dimensional parameters and unknown functions jointly. We establish consistency and derive the convergence rate of the estimator. We also show that the estimator of the finite dimensional parameters is $\sqrt n$-consistent, asymptotically normally distributed, and asymptotically efficient.

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