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Kernel Methods for Unimodality Test

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dc.contributor.advisor박병욱-
dc.contributor.author이선미-
dc.date.accessioned2017-07-14T00:31:33Z-
dc.date.available2017-07-14T00:31:33Z-
dc.date.issued2015-08-
dc.identifier.other000000053377-
dc.identifier.urihttp://hdl.handle.net/10371/121153-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 통계학과, 2015. 8. 박병욱.-
dc.description.abstractFinding the number of modes is of great interest in density estimation.
Well known nonparametric unimodality tests are including the dip test, excess mass test, and Silverman's test.
The dip and excess mass statistic are based on the empirical distribution and supremum distance, while Silverman's test depends on the bandwidth of kernel density estimator.
A main issue of these tests is conservatism and often calibration methods are used to address this issue.
We propose kernel methods of unimodality based on the dip and excess mass statistics to address the aforementioned issue.
We proposed to use the total variation distance to identify the closest unimodal distribution to kernel distribution and construct the kernel dip test based on the unimodal distribution from calculating test statistics.
Our numerical studies show that the proposed tests outperform.
We also introduce a kernel excess mass statistics.
Under the strong unimodal condition, the limiting distribution of the kernel excess mass statistic is the same as that of the empirical excess mass statistic.
However the numerical studies indicate that the calibration of kernel excess mass test has a greater power and better level accuracy than the calibration of empirical excess mass test.
We apply the proposed method to astronomy data, physical properties of minor planets in the solar system.
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dc.description.tableofcontentsList of Figures v
List of Tables vii
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Unimodality Test 4
2.1 The dip test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 The excess mass test . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Silverman's test . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 The Kernel Dip Test 14
3.1 The kernel dip with total variation . . . . . . . . . . . . . . . . 14
3.2 Computing the kernel dip . . . . . . . . . . . . . . . . . . . . . 20
3.3 The kernel dip test . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 The Kernel Excess Mass Test 36
4.1 The kernel excess mass . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Computing the kernel excess mass . . . . . . . . . . . . . . . . . 41
4.3 The kernel excess mass test . . . . . . . . . . . . . . . . . . . . 45
5 Numerical Study 48
5.1 Simulation 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2 Simulation 2 : Calibration tests . . . . . . . . . . . . . . . . . . 53
5.3 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6 Conclusion 68
Reference 70
Abstract in Korean 73
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dc.formatapplication/pdf-
dc.format.extent4576479 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectDensity estimation-
dc.subjectDip test-
dc.subjectExcess mass test-
dc.subjectKernel methods-
dc.subject.ddc519-
dc.titleKernel Methods for Unimodality Test-
dc.typeThesis-
dc.description.degreeDoctor-
dc.citation.pagesvii,74-
dc.contributor.affiliation자연과학대학 통계학과-
dc.date.awarded2015-08-
Appears in Collections:
College of Natural Sciences (자연과학대학)Dept. of Statistics (통계학과)Theses (Ph.D. / Sc.D._통계학과)
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