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題名 粗化數據之統計分析
Statistucal Analysis with Coarse Data
作者 陳宗萍
貢獻者 吳柏林
陳宗萍
關鍵詞 粗化數據
隨機集合
隸屬度函數
日期 2007
上傳時間 17-Sep-2009 13:46:17 (UTC+8)
摘要 本文討論在抽樣調查中被視為隨機集合模型的樣本，並試著架構基於模糊統計邏輯的粗化數據(coarse data)之理論與特性。因為有些抽樣調查中的數據可以視為隨機集合模型所得出的新數據。如何應用數學分析方法，配合軟計算技術以達到有效之資料處理與統計分析就是本研究之重點。我們將隨機抽樣樣本當作隨機實驗所做出來的結果，而這個論點可以幫助我們分析粗化數據。在探索抽樣調查的隨機集合和分佈的時候，機率測度論提供了很多種非精確數據給予統計學推測結論(statistical inference)，我們推廣傳統理論，以模糊集合及隸屬度為基礎，作為集合元素運算之依據。
關鍵字：粗化數據、隨機集合、隸屬度函數
In this paper we discuss the sample in the random set model for the sampling survey. Since the data from sampling survey can be treated as a new type of data from the random set model. How to apply the mathematical analyzing methods as well as soft computing techniques to reach an efficient propose is our main goal. We treat random sampling data as the result of random experimental design. And this concept will help us to analyze the coarse data. Finally, in investigating the random set and its distributions for the random sampling survey, traditional probability measure theory serves an important role in the statistical inference, while we use the membership function and fuzzy operations to extend traditional concept into a more general case.
Keywords： Coarse data, Random set, Membership function
參考文獻 1. Aigner, M. (1979), Combinatorial Theory, Springer-Verlag, N. Y.
2. Aumann, R. J. and Shapley, L. S. (1974), Values of Non-Atomic Games, Princeton University Press, Princeton, NJ.
3. Deville, J. C. and Sarndal, C. E. (1992), Calibration Estimators in Survey Sampling, Journal of the American Statistical Association 87, 376-382.
4. Foreman, E. K. (1991), Survey Sampling Principles, Marcel-Dekker, N. Y.
5. Georges, M. (1975), Random Sets and Integral Geometry, Wiley, N. Y.
6. Goodman, P. S. (1982), Social Comparison Processes in Organizations, In B. Staw and G. Salancik (Ends) New directions in organizational behavior, Malabar, FL: Krieger, 97-132.
7. Goutsias, J., Mahler, R., and Nguyen, H. T. (1997). Random Sets: Theory and Applications, Springer-Verlag, N. Y.
8. Hajek, J. (1981), Sampling from a Finite Population, Marcel-Dekker, N. Y.
9. Hartigan, J. A. (1975), Clustering Algorithms, Wiley.
10. Heitjan, D. F. and Rubin, D. B. (1991), Ignorability and Coarse Data, Ann. Math. Statis 23, 774-786.
11. Knottnerus, P. (2003), Sample Survey Theory, Springer-Verlag, N. Y.
12. Li, B. and Wang, T. (2004), Computational Aspects of the CAR Model and the Shapley Value, to appear in J. Information Sciences.
13. Mosteller, F. and Youtz, C. (1990), Quantifying Probabilistic Expressions, J. Statist. Sci 15, 2-34.
14. Nguyen, H. (2002), Random Sets for Statistics, Lukacs Lecture Notes, Bowling Green State University, Ohio.
15. Nguyen, H. (2005), An Introduction to Random Sets, Chapman and Hall/CRC, Boca Raton, Florida.
16. Nguyen, H. and Wang. T. (2004), A First Course in Probability and Statistics, Volume I, Tsinghua University Press, Beijing.
17. Nguyen, H. and Wu, B. (2006), Random and Fuzzy Sets in Coarse Data Analysis, Computational Statistics and Data Analysis 51, 70-85.
18. Norberg, T. (1992), On the Existence of Ordered Couplings of Random Sets with Applications, Israel J. Math 17, 241-264.
19. Robbins, H. E. (1944), On the Measure of a Random Set, Ann. Math. Statist 15, 70-74.
20. Sarndal, C. E., Swensson, B., and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlag, N. Y.
21. Zimmermann, H. J. (1991), Fuzzy Set Theory and its Applications, Kluwer, Dordrecht.
描述 碩士
國立政治大學
應用數學研究所
91751018
96
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091751018
資料類型 thesis
dc.contributor.advisor 吳柏林zh_TW
dc.contributor.author (Authors) 陳宗萍zh_TW
dc.creator (作者) 陳宗萍zh_TW
dc.date (日期) 2007en_US
dc.date.accessioned 17-Sep-2009 13:46:17 (UTC+8)-
dc.date.available 17-Sep-2009 13:46:17 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:46:17 (UTC+8)-
dc.identifier (Other Identifiers) G0091751018en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32571-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 91751018zh_TW
dc.description (描述) 96zh_TW
dc.description.abstract (摘要) 本文討論在抽樣調查中被視為隨機集合模型的樣本，並試著架構基於模糊統計邏輯的粗化數據(coarse data)之理論與特性。因為有些抽樣調查中的數據可以視為隨機集合模型所得出的新數據。如何應用數學分析方法，配合軟計算技術以達到有效之資料處理與統計分析就是本研究之重點。我們將隨機抽樣樣本當作隨機實驗所做出來的結果，而這個論點可以幫助我們分析粗化數據。在探索抽樣調查的隨機集合和分佈的時候，機率測度論提供了很多種非精確數據給予統計學推測結論(statistical inference)，我們推廣傳統理論，以模糊集合及隸屬度為基礎，作為集合元素運算之依據。
關鍵字：粗化數據、隨機集合、隸屬度函數		zh_TW
dc.description.abstract (摘要) In this paper we discuss the sample in the random set model for the sampling survey. Since the data from sampling survey can be treated as a new type of data from the random set model. How to apply the mathematical analyzing methods as well as soft computing techniques to reach an efficient propose is our main goal. We treat random sampling data as the result of random experimental design. And this concept will help us to analyze the coarse data. Finally, in investigating the random set and its distributions for the random sampling survey, traditional probability measure theory serves an important role in the statistical inference, while we use the membership function and fuzzy operations to extend traditional concept into a more general case.
Keywords： Coarse data, Random set, Membership function		en_US
dc.description.tableofcontents 1. 前言 1
2. 抽樣調查中的粗化集合 3
2. 1統計模型 3
2. 2 隨機集合和分佈 5
2. 3 粗化機制 6
3. 基於模糊集合架構之粗化數據 10
3. 1 隸屬度函數與模糊集合 10
3. 2 架構模糊統計與軟計算法 17
3. 3 顯著水準與擴大原理 22
3. 4模糊集合與隨機集合的關聯性 24
4. 結論 29
參考文獻 31		zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091751018en_US
dc.subject (關鍵詞) 粗化數據zh_TW
dc.subject (關鍵詞) 隨機集合zh_TW
dc.subject (關鍵詞) 隸屬度函數zh_TW
dc.title (題名) 粗化數據之統計分析zh_TW
dc.title (題名) Statistucal Analysis with Coarse Dataen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Aigner, M. (1979), Combinatorial Theory, Springer-Verlag, N. Y.zh_TW
dc.relation.reference (參考文獻) 2. Aumann, R. J. and Shapley, L. S. (1974), Values of Non-Atomic Games, Princeton University Press, Princeton, NJ.zh_TW
dc.relation.reference (參考文獻) 3. Deville, J. C. and Sarndal, C. E. (1992), Calibration Estimators in Survey Sampling, Journal of the American Statistical Association 87, 376-382.zh_TW
dc.relation.reference (參考文獻) 4. Foreman, E. K. (1991), Survey Sampling Principles, Marcel-Dekker, N. Y.zh_TW
dc.relation.reference (參考文獻) 5. Georges, M. (1975), Random Sets and Integral Geometry, Wiley, N. Y.zh_TW
dc.relation.reference (參考文獻) 6. Goodman, P. S. (1982), Social Comparison Processes in Organizations, In B. Staw and G. Salancik (Ends) New directions in organizational behavior, Malabar, FL: Krieger, 97-132.zh_TW
dc.relation.reference (參考文獻) 7. Goutsias, J., Mahler, R., and Nguyen, H. T. (1997). Random Sets: Theory and Applications, Springer-Verlag, N. Y.zh_TW
dc.relation.reference (參考文獻) 8. Hajek, J. (1981), Sampling from a Finite Population, Marcel-Dekker, N. Y.zh_TW
dc.relation.reference (參考文獻) 9. Hartigan, J. A. (1975), Clustering Algorithms, Wiley.zh_TW
dc.relation.reference (參考文獻) 10. Heitjan, D. F. and Rubin, D. B. (1991), Ignorability and Coarse Data, Ann. Math. Statis 23, 774-786.zh_TW
dc.relation.reference (參考文獻) 11. Knottnerus, P. (2003), Sample Survey Theory, Springer-Verlag, N. Y.zh_TW
dc.relation.reference (參考文獻) 12. Li, B. and Wang, T. (2004), Computational Aspects of the CAR Model and the Shapley Value, to appear in J. Information Sciences.zh_TW
dc.relation.reference (參考文獻) 13. Mosteller, F. and Youtz, C. (1990), Quantifying Probabilistic Expressions, J. Statist. Sci 15, 2-34.zh_TW
dc.relation.reference (參考文獻) 14. Nguyen, H. (2002), Random Sets for Statistics, Lukacs Lecture Notes, Bowling Green State University, Ohio.zh_TW
dc.relation.reference (參考文獻) 15. Nguyen, H. (2005), An Introduction to Random Sets, Chapman and Hall/CRC, Boca Raton, Florida.zh_TW
dc.relation.reference (參考文獻) 16. Nguyen, H. and Wang. T. (2004), A First Course in Probability and Statistics, Volume I, Tsinghua University Press, Beijing.zh_TW
dc.relation.reference (參考文獻) 17. Nguyen, H. and Wu, B. (2006), Random and Fuzzy Sets in Coarse Data Analysis, Computational Statistics and Data Analysis 51, 70-85.zh_TW
dc.relation.reference (參考文獻) 18. Norberg, T. (1992), On the Existence of Ordered Couplings of Random Sets with Applications, Israel J. Math 17, 241-264.zh_TW
dc.relation.reference (參考文獻) 19. Robbins, H. E. (1944), On the Measure of a Random Set, Ann. Math. Statist 15, 70-74.zh_TW
dc.relation.reference (參考文獻) 20. Sarndal, C. E., Swensson, B., and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlag, N. Y.zh_TW
dc.relation.reference (參考文獻) 21. Zimmermann, H. J. (1991), Fuzzy Set Theory and its Applications, Kluwer, Dordrecht.zh_TW