scholarly journals Moment Conditions Selection Based on Adaptive Penalized Empirical Likelihood

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Yunquan Song
Keyword(s):  
Empirical Likelihood ◽  
Real Life ◽  
Confidence Regions ◽  
Tuning Parameter ◽  
Finite Sample ◽  
Unknown Parameters ◽  
Moment Conditions ◽  
Moment Selection ◽  
Finite Sample Properties ◽  
Shrinkage Method

Empirical likelihood is a very popular method and has been widely used in the fields of artificial intelligence (AI) and data mining as tablets and mobile application and social media dominate the technology landscape. This paper proposes an empirical likelihood shrinkage method to efficiently estimate unknown parameters and select correct moment conditions simultaneously, when the model is defined by moment restrictions in which some are possibly misspecified. We show that our method enjoys oracle-like properties; that is, it consistently selects the correct moment conditions and at the same time its estimator is as efficient as the empirical likelihood estimator obtained by all correct moment conditions. Moreover, unlike the GMM, our proposed method allows us to carry out confidence regions for the parameters included in the model without estimating the covariances of the estimators. For empirical implementation, we provide some data-driven procedures for selecting the tuning parameter of the penalty function. The simulation results show that the method works remarkably well in terms of correct moment selection and the finite sample properties of the estimators. Also, a real-life example is carried out to illustrate the new methodology.

ADAPTIVE GMM SHRINKAGE ESTIMATION WITH CONSISTENT MOMENT SELECTION

2013 ◽  
Vol 29 (5) ◽  
pp. 857-904 ◽  
Author(s):  
Zhipeng Liao
Keyword(s):  
Political Economy ◽  
Labor Supply ◽  
Generalized Method Of Moments ◽  
Finite Sample ◽  
Unknown Parameters ◽  
Moment Conditions ◽  
Oracle Properties ◽  
Moment Selection ◽  
Finite Sample Properties ◽  
Shrinkage Method

This paper proposes a generalized method of moments (GMM) shrinkage method to efficiently estimate the unknown parameters θo identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties; i.e., it consistently selects the correct moment conditions in the second set and at the same time, its estimator is as efficient as the GMM estimator based on all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify θo. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981, Journal of Political Economy 89(6), 1059–1085) and Altonji (1986, Journal of Political Economy 94(3), 176–215). Our empirical findings support the validity of the instrumental variables used in both papers and confirm that wage is an endogenous variable in the labor supply equation.

scholarly journals Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hanji He ◽  
Guangming Deng
Keyword(s):  
Empirical Likelihood ◽  
Missing At Random ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
High Dimensional ◽  
Finite Sample ◽  
The Mean ◽  
Data Missing ◽  
Consistency And Asymptotic Normality ◽  
The Impact

We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.

scholarly journals Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

2022 ◽  
Vol 9 ◽  
Author(s):  
Xiuzhen Zhang ◽  
Riquan Zhang ◽  
Zhiping Lu
Keyword(s):  
Time Series ◽  
Empirical Likelihood ◽  
Long Memory ◽  
Score Function ◽  
Real Data ◽  
Confidence Regions ◽  
Stationary Time Series ◽  
Time Series Models ◽  
Finite Sample ◽  
Memory Time

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

TESTING FOR NONNESTED CONDITIONAL MOMENT RESTRICTIONS VIA CONDITIONAL EMPIRICAL LIKELIHOOD

2010 ◽  
Vol 27 (1) ◽  
pp. 114-153 ◽  
Author(s):  
Taisuke Otsu ◽  
Yoon-Jae Whang
Keyword(s):  
Empirical Likelihood ◽  
Finite Sample ◽  
Conditional Moment ◽  
Null Distributions ◽  
Finite Dimensional ◽  
Global Power ◽  
Finite Sample Properties ◽  
The Moment ◽  
Moment Restrictions ◽  
Power Properties

We propose nonnested tests for competing conditional moment restriction models using the method of conditional empirical likelihood, recently developed by Kitamura, Tripathi, and Ahn (2004) and Zhang and Gijbels (2003). To define the test statistics, we use the implied conditional probabilities from conditional empirical likelihood, which take into account the full implications of conditional moment restrictions. We propose three types of nonnested tests: the moment-encompassing, Cox-type, and efficient score-encompassing tests. We derive the asymptotic null distributions and investigate their power properties against a sequence of local alternatives and a fixed global alternative. Our tests have distinct global power properties from some of the existing tests based on finite-dimensional unconditional moment restrictions. Simulation experiments show that our tests have reasonable finite sample properties and dominate some of the existing nonnested tests in terms of size-corrected powers.

scholarly journals Count Data Time Series Modelling in Julia—The CountTimeSeries.jl Package and Applications

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 666
Author(s):  
Manuel Stapper
Keyword(s):  
Time Series ◽  
Real Life ◽  
Theoretical Background ◽  
Information Criteria ◽  
Finite Sample ◽  
Ml Estimation ◽  
Real Life Data ◽  
Time Series Modelling ◽  
Finite Sample Properties ◽  
Count Data Time Series

A new software package for the Julia language, CountTimeSeries.jl, is under review, which provides likelihood based methods for integer-valued time series. The package’s functionalities are showcased in a simulation study on finite sample properties of Maximum Likelihood (ML) estimation and three real-life data applications. First, the number of newly infected COVID-19 patients is predicted. Then, previous findings on the need for overdispersion and zero inflation are reviewed in an application on animal submissions in New Zealand. Further, information criteria are used for model selection to investigate patterns in corporate insolvencies in Rhineland-Palatinate. Theoretical background and implementation details are described, and complete code for all applications is provided online. The CountTimeSeries package is available at the general Julia package registry.

Weighted-Correct Empirical likelihood for Linear EV Models

2012 ◽  
Vol 524-527 ◽  
pp. 3884-3887
Author(s):  
Yu Ying Jiang ◽  
Xiao Feng Zhu
Keyword(s):  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Estimation Procedure ◽  
Confidence Regions ◽  
Likelihood Inference ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Chi Square ◽  
Missing Responses ◽  
Ev Model

The empirical likelihood inference based weighted correction in linear EV model with missing responses is studied. A weighted-correct empirical likelihood method is developed. It can be shown that the weighted-correct empirical likelihood ratio is asymptotically standard chi-square. The results can be used directly to construct the asymptotic confidence regions of the unknown parameters. The estimation procedure is relatively simple and the estimated efficiency has been greatly improved.

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