A New Winsorized x^(2) Statistic and Its Behavior

전반적으로 사용되어지는 대부분의 통계 추론 절차는 모집단의 오차분포가 정규분포라는 가정 하에서 전개된다. 그러나 모집단의 오차분포가 정규분포보다 더 긴 꼬리를 갖을 때 이러한 통계 절차들은 더 이상 로버스트하지 않고 심각한 이상점이 존재할 경우 검정력의 손실은 상당하다. 본 논문에서는 모분산의 추정을 위해 로버스트한 새로운 윈저화 카이 제곱 통계량을 제안하였다. 특히 위꼬리 부분에서 n-2g-1 크기의 자유도를 갖는 기존의 카이 제곱 분포와 잘 근사되도록 통계량을 고안하였다. 그리고 이러한 결과를 적용하여 로버스트한 F 통계량을 구성하였다. 이렇게 제안된 새로운 통계량의 분포는 몬테 칼로 모의 실험 기법을 이용하여 경험적 분포로 제시하였다.;Most statistical inference procedures which have been developed so far and are utilized widely in the real world are formed by a critical assumption that the underlying error distribution is Gaussian. However the typical shape of an error distribution has rather heavy tails, though symmetry is preserved. Therefore classical inferential procedures based on sample mean and variance lack robustness for such a non-normal situation. Especially in the presence of severe outliers, they lose considerble amount of power. In this thesis we propose a robust statistic for estimating the population variance; namely, a Winsorized chi-square statistic which can be well approximated to a usual chi-square distribution with (n-2g-1) degrees of freedom, particularly in the region of quantiles associated with low significance probabilities. And then we apply this result to form a robust F statistic. We also explore their empirical distributions by utilizing the Monte-Carlo simulation technique.CONTENTS ABSTRACT Chapter 1 Introduction and Literature Review = 1 Chapter 2 A New Winsorized Chi-square Statistic = 6 Chapter 3 Construction of a Pseudo-F Statistic = 12 Chapter 4 Final Remarks = 16 BIBLIOGRAPHY = 18 APPENDIX A Program, Tables and Graphs for Chapter 2 = 20 A.1. SAS macro = 20 A.2. Tables of the empirical distribution = 24 A.3. Graphs of the empirical distribution = 27 APPENDIX B Program and Tables for Chapter 3 = 30 B.1. SAS macro = 30 B.2. Tables of the empirical distribution = 33 논문초록 = 38 감사의 글 = 3

초기 홀로세 동안 천 년 시간규모에서의 대기 중 이산화탄소 변동성

학위논문 (석사)-- 서울대학교 대학원 : 지구환경과학부, 2014. 2. 안진호.The objective of this study is to decipher the relationship between climate and carbon cycles on millennial time scales during the early Holocene. The early Holocene (11.7–7.0 ka) is a climatically dynamic period on millennial timescales as seen in paleoproxy records for ice sheet collapse (Bond Cycle) in the North Atlantic, sea ice extent variations in the Southern Ocean, and El Niño–like and La Niña–like variation in the eastern equatorial Pacific. We may expect atmospheric CO2 concentration change during the early Holocene because CO2 is controlled by physical and biological processes in ocean and land. However, existing CO2 records from EPICA Dome C and Taylor Dome ice cores do not address the issue due to lack of sufficient temporal resolution and chronology. In this study, a new Siple Dome CO2 record for the time period of 9.0-11.7 ka is obtained. Combined with an existing Siple Dome CO2 record for 7.3-9.0 ka, a high-resolution CO2 record for the early Holocene (7.3-11.7 ka) is constructed. The sampling resolution is better than 30 years for 11.7–7.3 ka. The Siple Dome CO2 data show a decrease of CO2 of ~10 ppm from 10.9 to 7.3 ka and multi-centennial to millennial variability of 2-6 ppm with local minima at 11.1, 10.1, 9.0 and 8.3 ka. The millennial-scale CO2 variation correlates with paleoclimate records and show that atmospheric CO2 change was in harmony with global climate change. Possible control mechanisms for CO2 variations are discussed.Abstract Table of contents List of tables List of figures 1. Introduction 1 2. Methods 5 2.1. Siple Dome ice core recovery 5 2.2. Dry gas extraction 5 2.3. Gas Chromatography 7 2.4. Data corrections 9 2.4.1. Blank test 9 2.4.2. Gravitational fractionation effect 10 2.5. Siple Dome chronology 10 3. Results 13 3.1. Data quality 13 3.2. General features 13 3.3. Relationship between climate and CO2 14 4. Climate and carbon cycle 16 4.1. Perturbation in the Southern Ocean 17 4.2. Perturbation in AMOC 19 4.3. El Nio-like and Na Nia-like climate variation 21 5. Discusstion 23 5.1. Comparisons CO2 records among ice cores 23 5.2. Future studies 25 6. Conclusion 28 References 29 Tables 41 Figures 45 Abstract in korean 57Maste