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Pairwise Comparison Model with a Diverging Number of Nuisance Parameters : 장애모수의 수가 증가하는 쌍별 비교모형
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 김용대 | - |
dc.contributor.author | 전종준 | - |
dc.date.accessioned | 2017-07-14T00:30:29Z | - |
dc.date.available | 2017-07-14T00:30:29Z | - |
dc.date.issued | 2012-08 | - |
dc.identifier.other | 000000004482 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121136 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 통계학과, 2012. 8. 김용대. | - |
dc.description.abstract | We consider a ranking problem of players in a game where the number of
players diverges but the number of games per player is ¯xed. The standard maximum likelihood estimator based on Thurstone model is inconsistent since the number of nuisance parameters (i.e. the ability of each player) diverges. We propose a new estimator based on the conditional likelihood. We propose a conditional pairwise comparison likelihood and prove that the maximum conditional likelihood estimator is consistent. Also, we develop an e±cient computational algorithm to calculate the maximum conditional likelihood. We illustrate the proposed method on data generated from a game called the Skid Rush that is a web based multi-player car racing game. | - |
dc.description.tableofcontents | 1 Introduction 1
2 Probability Model for Ranking 2.1 Probability Model Space for ranking 2.2 Thurstone Model 2.3 Bradley Terry Model 2.4 Model for the car racing 3 Thurstone Ranking Model through the Pairwise Comparison Method 3.1 Relation between Thursone Model and Bradley Terry Model 3.2 Asymptotics 3.3 Extension of Thustone Model 4 Pairwise Comparison model with a diverging number of nuisance parameters 4.1 Bradley-Terry model with the diverging number of nuisance parameters 4.2 Conditional pairwise comparison likelihood 4.3 Asymptotics 5 Simulation and Real Data Analysis 44 5.1 Computation 5.2 Numerical Analysis 5.3 Real data analysis 6 Conclusion 59 | - |
dc.format | application/pdf | - |
dc.format.extent | 549914 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Ranking model | - |
dc.subject | Pairwise comparison | - |
dc.subject | high dimension | - |
dc.title | Pairwise Comparison Model with a Diverging Number of Nuisance Parameters | - |
dc.title.alternative | 장애모수의 수가 증가하는 쌍별 비교모형 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Jong-June Joen | - |
dc.description.degree | Doctor | - |
dc.citation.pages | LXV, 65 | - |
dc.contributor.affiliation | 자연과학대학 통계학과 | - |
dc.date.awarded | 2012-08 | - |
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