Maximum empirical likelihood estimation in U-statistics based general estimating equations

<p>In the first part of this thesis, we study maximum empirical likelihood estimates (MELE's) in U-statistics based general estimating equations (UGEE's). Our technical maneuver is the jackknife empirical likelihood (JEL) approach. We give the local uniform asymptotic normality condition for the log-JEL for UGEE's. We derive the estimating equations for finding MELE's and provide their asymptotic normality. We obtain easy MELE's which have less computational burden than the usual MELE's and can be easily implemented using existing software. We investigate the use of side information of the data to improve efficiency. We exhibit that the MELE's are fully efficient, and the asymptotic variance of a MELE will not increase as the number of UGEE's increases. We give several important examples and demonstrate that efficient estimates of moment based distribution characteristics in the presence of side information can be obtained using JEL for U-statistics.</p> <p>In the second part, we propose several JEL goodness-of-fit tests for spherical symmetry, rotational symmetry, antipodal symmetry, coordinatewise symmetry and exchangeability. We employ the jackknife empirical likelihood for vector U-statistics to incorporate side information. We use estimated constraint functions and allow the number of constraints and the dimension to grow with the sample size so that these tests can be used to test hypotheses for high dimensional symmetries. We demonstrate that these tests are distribution free and asymptotically chisquare distributed. We conduct extensive simulations to evaluate the performance of these tests.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2016

Author dc:creator

• Li, Lingnan

Contributors dc:contributor

• Hanxiang Peng
• Benzion Boukai
• Guang Cheng
• Wei Zheng

• Pure sciences
• Jackknife pseudo value
• Maximum empirical likelihood estimate
• U-statistics
• U-statistics based general estimating equations
• Mathematics
• Statistics and Probability

Repository record dc:identifier

https://docs.lib.purdue.edu/open_access_dissertations/796

OAI identifier oai:identifier

oai:docs.lib.purdue.edu:open_access_dissertations-1988