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Time-dynamic Varying Coefficient Models for Longitudinal Data
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 박병욱 | - |
dc.contributor.author | 이경은 | - |
dc.date.accessioned | 2017-07-14T00:31:55Z | - |
dc.date.available | 2017-07-14T00:31:55Z | - |
dc.date.issued | 2016-02 | - |
dc.identifier.other | 000000133537 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121160 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 통계학과, 2016. 2. 박병욱. | - |
dc.description.abstract | In this thesis, we propose a varying coefficient model that can be applied to longitudinal or functional data. The varying coefficient model captures the relationship between the response and the covariates with coefficient functions that are affected by smoothing variables. The varying coefficient model is a structured nonparametric model, and it can easily interpret the effects of the covariates. To avoid the curse of dimensionality, we propose the time-dynamic varying coefficient model as a structured nonparametric model. Also, we construct an iterative algorithm for estimation by extending the smooth backfitting method so that the estimator is defined as a projection of the full-dimensional estimator onto the additive function space with $L_2$-sense. We show that the proposed algorithm achieves uniform convergence with exponential rate and then study the asymptotic property of the estimator. Based on the numerical study of performances, we apply air quality data to the time-dynamic varying coefficient model for a real data analysis. | - |
dc.description.tableofcontents | 1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Varying Coecient Models . . . . . . . . . . . . . . . . . . . . . 4 1.3 Nonparametric Models for Longitudinal Data . . . . . . . . . . 6 1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Methodology 11 2.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Backfitting Equation . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Asymptotic Properties 17 3.1 Convergence of Backfitting . . . . . . . . . . . . . . . . . . . . . 17 3.2 Asymptotic Distribution . . . . . . . . . . . . . . . . . . . . . . 22 4 Numerical Studies 25 4.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Real Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 36 5 Technical Details 41 List of Notations 50 References 53 Abstract in Korean 59 | - |
dc.format | application/pdf | - |
dc.format.extent | 874881 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Kernel smoothing | - |
dc.subject | Longitudinal data | - |
dc.subject | Smooth backfitting | - |
dc.subject | Varying coefficient models | - |
dc.subject.ddc | 519 | - |
dc.title | Time-dynamic Varying Coefficient Models for Longitudinal Data | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.citation.pages | vii, 59 | - |
dc.contributor.affiliation | 자연과학대학 통계학과 | - |
dc.date.awarded | 2016-02 | - |
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