{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101162"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101162","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Essays on misspecified models","abstract":"This thesis identifies the asymptotic properties of generalized empirical likelihood estimators when moment conditions are not correctly specified. Classical generalized empirical likelihood estimators rely on the correct moment conditions, however, those conditions are mostly generated from economic theory and some of them are not testable. Hence, it is needed to understand the property of the estimators and test statistics when moments are misspecified and provide robust estimators and test statistics when moment conditions are misspecified. Chapter 1, ”Robust Inference for Instrumental Variable Models with Locally Non-exogenous Instruments”, highlights that conventional tests often fail to give accurate inferences when exogeneity conditions are mildly violated in instrumental variable models. The sizes of those tests can be considerably distorted due to their non-centrally distributed test statistics un- der the null hypothesis. This paper proposes an adjusted score-type test to correct this size distortion while preserving good discriminatory power. We prove that under the null hypothesis, this adjusted score-type test statistic converges to a central chi-squared distribution and thus is not adversely affected by local non-exogeneity. Furthermore, the Monte Carlo simulations confirm that our newly proposed test has considerable size improvement over the conventional ones, while their power is not very different. Chapter 2, ”Mis-specification-Robust Bootstrap for Empirical Likelihood Estimators ”, proposes an adapted bootstrap testing procedure for empirical likelihood estimators. This method extends the bootstrap method in Lee (2014) by using the empirical likelihood weights, which could improve the efficiency if the moment condition model is correctly specified. This proposed bootstrap method is also robust to model misspecification as shown in Lee (2014). The first-order asymptotic validity of the proposed procedure is shown, and multiple Monte Carlo Studies are conducted to support the theoretical findings. Chapter 3, ”Higher Order MSE Comparisons of Generalized Empirical Likelihood Estimators”, calculates the higher order asymptotic mean square errors (MSE) of generalized empirical likelihood (GEL) estimators on a simple linear model. It is well known from Newey and Smith (2004) that the Empirical likelihood (EL) estimator has the smallest higher-order asymptotic bias among the GEL estimators; however, in this paper we find that the EL estimator no longer has this property for the criteria of MSE. We propose a data-driven method to achieve the least asymptotic higher-order MSE in the GEL family.","abstract_html":"This thesis identifies the asymptotic properties of generalized empirical likelihood estimators when moment conditions are not correctly specified. Classical generalized empirical likelihood estimators rely on the correct moment conditions, however, those conditions are mostly generated from economic theory and some of them are not testable. Hence, it is needed to understand the property of the estimators and test statistics when moments are misspecified and provide robust estimators and test statistics when moment conditions are misspecified. Chapter 1, ”Robust Inference for Instrumental Variable Models with Locally Non-exogenous Instruments”, highlights that conventional tests often fail to give accurate inferences when exogeneity conditions are mildly violated in instrumental variable models. The sizes of those tests can be considerably distorted due to their non-centrally distributed test statistics un- der the null hypothesis. This paper proposes an adjusted score-type test to correct this size distortion while preserving good discriminatory power. We prove that under the null hypothesis, this adjusted score-type test statistic converges to a central chi-squared distribution and thus is not adversely affected by local non-exogeneity. Furthermore, the Monte Carlo simulations confirm that our newly proposed test has considerable size improvement over the conventional ones, while their power is not very different. Chapter 2, ”Mis-specification-Robust Bootstrap for Empirical Likelihood Estimators ”, proposes an adapted bootstrap testing procedure for empirical likelihood estimators. This method extends the bootstrap method in Lee (2014) by using the empirical likelihood weights, which could improve the efficiency if the moment condition model is correctly specified. This proposed bootstrap method is also robust to model misspecification as shown in Lee (2014). The first-order asymptotic validity of the proposed procedure is shown, and multiple Monte Carlo Studies are conducted to support the theoretical findings. Chapter 3, ”Higher Order MSE Comparisons of Generalized Empirical Likelihood Estimators”, calculates the higher order asymptotic mean square errors (MSE) of generalized empirical likelihood (GEL) estimators on a simple linear model. It is well known from Newey and Smith (2004) that the Empirical likelihood (EL) estimator has the smallest higher-order asymptotic bias among the GEL estimators; however, in this paper we find that the EL estimator no longer has this property for the criteria of MSE. We propose a data-driven method to achieve the least asymptotic higher-order MSE in the GEL family.","abstract_has_math":false,"creators":["Zuo, Bing"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Economics","degree_department":null,"school":null,"contributors":["Bera, Anil","Shao, Xiaofeng","Lee, JiHyung","Chung, Eun Yi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-04T20:34:04Z","date_published":"2018-09-04T20:34:04Z","updated_at":"2026-07-22T22:24:38Z","subjects":["Generalized Emperical Likelihood, Moment Conditions"],"languages":["en"],"rights":["Copyright 2018 Bing Zuo"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101162","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bera, Anil","Shao, Xiaofeng","Lee, JiHyung","Chung, Eun Yi"]},{"key":"dc:creator","label":"Author","values":["Zuo, Bing"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-04T20:34:04Z","2020-09-05T09:15:13Z","2018-04-15","2018-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Economics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Generalized Emperical Likelihood, Moment Conditions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Bing Zuo"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101162"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis identifies the asymptotic properties of generalized empirical likelihood estimators when moment conditions are not correctly specified. Classical generalized empirical likelihood estimators rely on the correct moment conditions, however, those conditions are mostly generated from economic theory and some of them are not testable. Hence, it is needed to understand the property of the estimators and test statistics when moments are misspecified and provide robust estimators and test statistics when moment conditions are misspecified. Chapter 1, ”Robust Inference for Instrumental Variable Models with Locally Non-exogenous Instruments”, highlights that conventional tests often fail to give accurate inferences when exogeneity conditions are mildly violated in instrumental variable models. The sizes of those tests can be considerably distorted due to their non-centrally distributed test statistics un- der the null hypothesis. This paper proposes an adjusted score-type test to correct this size distortion while preserving good discriminatory power. We prove that under the null hypothesis, this adjusted score-type test statistic converges to a central chi-squared distribution and thus is not adversely affected by local non-exogeneity. Furthermore, the Monte Carlo simulations confirm that our newly proposed test has considerable size improvement over the conventional ones, while their power is not very different. Chapter 2, ”Mis-specification-Robust Bootstrap for Empirical Likelihood Estimators ”, proposes an adapted bootstrap testing procedure for empirical likelihood estimators. This method extends the bootstrap method in Lee (2014) by using the empirical likelihood weights, which could improve the efficiency if the moment condition model is correctly specified. This proposed bootstrap method is also robust to model misspecification as shown in Lee (2014). The first-order asymptotic validity of the proposed procedure is shown, and multiple Monte Carlo Studies are conducted to support the theoretical findings. Chapter 3, ”Higher Order MSE Comparisons of Generalized Empirical Likelihood Estimators”, calculates the higher order asymptotic mean square errors (MSE) of generalized empirical likelihood (GEL) estimators on a simple linear model. It is well known from Newey and Smith (2004) that the Empirical likelihood (EL) estimator has the smallest higher-order asymptotic bias among the GEL estimators; however, in this paper we find that the EL estimator no longer has this property for the criteria of MSE. We propose a data-driven method to achieve the least asymptotic higher-order MSE in the GEL family.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2020-05-01","The student, Bing Zuo, accepted the attached license on 2018-04-13 at 10:44.","The student, Bing Zuo, submitted this Dissertation for approval on 2018-04-13 at 10:52.","This Dissertation was approved for publication on 2018-04-15 at 10:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12232 on 2018-08-31 at 17:18:38","Made available in DSpace on 2018-09-04T20:34:04Z (GMT). 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Classical generalized empirical likelihood estimators rely on the correct moment conditions, however, those conditions are mostly generated from economic theory and some of them are not testable. Hence, it is needed to understand the property of the estimators and test statistics when moments are misspecified and provide robust estimators and test statistics when moment conditions are misspecified. Chapter 1, ”Robust Inference for Instrumental Variable Models with Locally Non-exogenous Instruments”, highlights that conventional tests often fail to give accurate inferences when exogeneity conditions are mildly violated in instrumental variable models. The sizes of those tests can be considerably distorted due to their non-centrally distributed test statistics un- der the null hypothesis. This paper proposes an adjusted score-type test to correct this size distortion while preserving good discriminatory power. We prove that under the null hypothesis, this adjusted score-type test statistic converges to a central chi-squared distribution and thus is not adversely affected by local non-exogeneity. Furthermore, the Monte Carlo simulations confirm that our newly proposed test has considerable size improvement over the conventional ones, while their power is not very different. Chapter 2, ”Mis-specification-Robust Bootstrap for Empirical Likelihood Estimators ”, proposes an adapted bootstrap testing procedure for empirical likelihood estimators. This method extends the bootstrap method in Lee (2014) by using the empirical likelihood weights, which could improve the efficiency if the moment condition model is correctly specified. This proposed bootstrap method is also robust to model misspecification as shown in Lee (2014). The first-order asymptotic validity of the proposed procedure is shown, and multiple Monte Carlo Studies are conducted to support the theoretical findings. Chapter 3, ”Higher Order MSE Comparisons of Generalized Empirical Likelihood Estimators”, calculates the higher order asymptotic mean square errors (MSE) of generalized empirical likelihood (GEL) estimators on a simple linear model. It is well known from Newey and Smith (2004) that the Empirical likelihood (EL) estimator has the smallest higher-order asymptotic bias among the GEL estimators; however, in this paper we find that the EL estimator no longer has this property for the criteria of MSE. We propose a data-driven method to achieve the least asymptotic higher-order MSE in the GEL family.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2020-05-01","The student, Bing Zuo, accepted the attached license on 2018-04-13 at 10:44.","The student, Bing Zuo, submitted this Dissertation for approval on 2018-04-13 at 10:52.","This Dissertation was approved for publication on 2018-04-15 at 10:10.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12232 on 2018-08-31 at 17:18:38","Made available in DSpace on 2018-09-04T20:34:04Z (GMT). No. of bitstreams: 2 ZUO-DISSERTATION-2018.pdf: 537836 bytes, checksum: 35336de7037037c872aedb5d8cff1cc0 (MD5) LICENSE.txt: 4205 bytes, checksum: 99211691f3a302635239459d26781b80 (MD5) Previous issue date: 2018-04-15","Embargo set by: Seth Robbins for item 107245 Lift date: 2020-09-04T20:34:13Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 107245 Lift date: 2020-09-04T20:37:00Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 107245 Lift date: 2020-09-04T20:42:08Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 107245 on 2020-09-05T09:15:13Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/101162"],"dc:language":["en"],"dc:rights":["Copyright 2018 Bing Zuo"],"dc:subject":["Generalized Emperical Likelihood, Moment Conditions"],"dc:title":["Essays on misspecified models"],"dc:type":["text"],"thesis:degree_discipline":["Economics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:38Z"}