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| 研究生： |
江上立 Jiang, Shang-Li |
|---|---|
| 論文名稱： |
數學規劃在統計問題上應用之研究 無 |
| 指導教授： | 李子壩 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 1977 |
| 畢業學年度： | 66 |
| 語文別： | 中文 |
| 論文頁數： | 84 |
| 中文關鍵詞： | 無 |
| 相關次數： | 點閱：119 下載：0 |
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緒言1
第一章 數學規劃和多變量統計之關係3
第一節 緒言3
第二節 數學規劃和多變量統計之關係4
第三節 數學規劃模式7
第四節 綫性迴歸模式10
第二章 綫性迴歸分析13
第一節 緒言13
第二節 無條件式限制的情形13
第三節 有條件式限制的情形19
第四節 條件式含不等號的情形24
第三章 綫性規劃方法在綫性迴歸上之應用29
第一節 緒言29
第二節 採用L2長度的綫性迴歸問題29
第三節 採用L1長度的綫性迴歸問題30
第四節 採用L∞長度的綫性迴歸問題34
第四章 非綫性規劃在綫性迴歸和非終性迴歸上之應用37
第一節 緒言37
第二節 用各種不同標準解綫性迴歸問題37
第三節 用各種不同標準解非綫性迴歸問題41
第四節 最概法43
第五章 利用數學規劃來解統計問題的進一步研究45
第一節 緒言45
第二節 Lp配合和推定45
第三節 Rice教授和White教授的實證分析53
第四節 Kiountzis教授研究L1長度之偏誤性的實證分析60
第五節 均等分佈、常態分佈和拉普拉斯分佈的最概推定量62
第六章 綫性模式的不偏推定之一種新的綫性規劃步驟66
第一節 緒言66
第二節 求L1長度的不偏推定量之步驟71
第三節 求L∞長度的不偏推定量之步驟71
第七章 實例74
結論77
1. Anderson, T.W., An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, Inc., 1958.
2. Ashar, V. G. & Wallace, T. D., “A sampling study of minimum absolute deviations estimators”, O. R., Vol. II, pp 747-758, 1963.
3. Ben- Israel, A. & Charnes, A., "" An explicit solution of a special class of linear programming problems"", O.R., Vol. 16, pp 1166- 1175, 1968.
4. Bracken, J. & McCormick, G.P., Selected Applications of Nonlinear Programming, John Wiley & Sons, Inc., 1968.
5. Carpenter, O., “Nate on the extension of Craig’s theorem to non-central variates”, Ann. Math. Stat., Vol. 21, pp 455-57, 1950.
6. Charnes, A.& Cooper, W.W., “ Optimal estimation of executive compensation by linear programming, Management Science, Vol. 1, pp 138-151,1955.
7. Chipman, J.S. & Rao, M.M., "" The treatment of linear restrictions in regression analysis"", Econometrica, Vol. 32, pp 198- 209, 1964.
8. Cooper, L. & Steinberg, D., Linear Programming, W. B. Saunders Co., 1974.
9. Cramer, H., Mathematical Methods of Statistics, Princeton University Press, 1946.
10. Dantzig, G. B., Linear Programming and Extensions, Princeton University Press, 1963.
11. Dantzig, G.B., “Upper bounds, secondary constraints, and block triangularity in linear programming”, Econometrica, Vol. 23, pp 174-183, 1954.
12. Dorn, W.S., “Duality in guadratic programming”, Quarterly Appl. Math., Vol.18, pp 155-161, 1960.
13. Draper, N. R. & Smith, H., Applied Regression Analysis, John Wiley & Sons, Inc., 1966.
14. Durbin, J., ” A note on regression when there is extraneous information about one of the coefficients”, J. A. S. A., Vol.48, pp 799-808, 1953.
15. Dwyer, P. S., : ”Generalizations of a Gaussian Theorem”, Ann. Math. Stat., Vol. 29, pp 106-117, 1958.
16. Goldberger, A. S., Econometric Theory, John Wiley & Sons, Inc., 1964.
17. Hajek, J., A Couse in Nonparametric Statistics, Holden-Day, 1969.
18. Hartley, H. O., “The modified Gauss-Newton method for the fitting of non-linear regression functions by least square”, Technometrics, Vol. 3, pp 269-280, 1961.
19. Himmelblan, D.M, Applied Nonlinear Programming, Mc- Craw-Hill, 1972.
20. Judge, C. G. & Takayama, T., “ Inequality restrictions in regression analysis”, J.A.S.A., Vol. 61, pp 166-181,1966.
21. Karst, O. J., “ Linear curve fitting using least deviations”, J.A.S.A., Vol. 53, pp 118-132, 1958.
22. Kelley, J. E., “An application of linear programming to curve fitting”, J. Soc. Indust. Appl. Math., Vol. 6, pp15- 21, 1958.
23. Kiountouzis, E.A., ” Linear Programming techniques in regression analysis”, Appl. Stat., Vol. 22, pp69-73, 1973.
24. Mantel, M., ” Restricted least square regression and convex quadratic programming”, Thchnometrics, Vol 11, pp 763- 773, 1969.
25. McMillan, C., Mathematical Programming, John Wiley & Sons, Inc., 1970.
26. Mood, A.M. & Graybill, F.A. & Boes, D.C., Intro, to the Theory of Statistics, McGraw-Hill, Inc., 1974.
27. Rice, J.R. & White, J.S., ” Norms for smoothing and estimation”, S.I.A.M. Review, Vol. 6, pp 243-255, 1964.
28. Robers, P. D., “An interval programming algorithm for discrete linear L. approximation problems”, J. Approx. Theory, Vol. 2, pp 323-336, 1969.
29. Searle, S. R., Linear Models, John Wiley & Sons, Inc., 1971.
30. Siddigui, M. M., “Approximations to the moments of the sample median”, Ann. Math. Stat., Vol. 33, pp 157-168, 1962.
31. Sielken, R. L. & Hartley, H. O., “ Two linear programming algorithms for unbiased estimation of linear models”, J.A. S.A. Vol. 68, pp 639-641, 1973.
32. Simonnard, M., Linear Programming, Prentice-Hall, Inc.,1966.
33. Sposito, V.A., Linear and Nonlinear Programming, The Iowa State University Press, 1975.
34. Theil, H., Economic Forcasts and Policy, North-Holland, 1961.
35. Theil, H., “ On the use of incomplete prior information in regression analysis“, J.A.S.A., Vol. 58, pp 401-414, 1963.
36. Wagner, H.M., “ Linear Programming techniques for regression analysis“, J.A.S.A., Vol. 54, pp 206-212, 1959.
37. Wegner, P., “ Relations between multivariate statistics and mathematical programming “, Appl. Stat., Vol. 12, pp 146- 150, 1963.
38. Wilka, S. S., Mathematical Statistics, John Wiley & Sons, Inc., 1962.
39. Wolfe, P., “The simplex method for quadratic programming”, Econometerica, Vol. 27, pp 382-398, 1959.
40. Zangwill, W. I., Nonlinear Programming, Prentice-Hall, Inc., 1967.
41.陳正澄：計量經濟學。台北，1974。
42.陳超塵：統計學原理。台北，1969。
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