博碩士論文 88225014 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:12 、訪客IP:3.227.2.246
姓名 林哲揚(Che-Yang Lin)  查詢紙本館藏   畢業系所 統計研究所
論文名稱 離散資料中改良p-值之研究
(The study of the improved p-value test in discrete distributions.)
相關論文
★ 邊際模式隱藏分類分析★ 2×2列聯表中雙尾檢定p-值之研究
★ 2×2列聯表多項分布獨立性檢定之研究★ 台灣地區暴力犯罪研究
★ 暴力犯罪與嫌疑人特徵之研究★ 老人生活滿意度之研究
★ 老人福利需求之研究★ 中老人罹患主要疾病之研究
★ 中老年對安養機構重要性之分析★ 中老年人對經濟補助重要性因素之分析
★ 中老年人罹患主要慢性疾病特徵之研究★ 搶奪現行犯嫌疑人特徵之研究
★ 國家風景特定區之服務品質與遊客滿意度之研究★ 國道高速公路服務區之隱性服務要素滿意度研究
★ 污水下水道廢水水質指標關係之研究★ 戶中選樣之研究
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) p-值在統計學上有相當廣泛的應用,
但是對離散資料的統計推論,
虛無假設成立時之模型經常含有干擾參數,
使得p-值的性質較為複雜.
本論文針對一般常用於離散資料分析之檢定提出一改良方法,
若使用p-值進行檢定,
本論文所提出之方法是以該p-值做為檢定統計量,
並使用正確非條件方法以構造改良p-值檢定.
對於兩獨立二項抽樣母體成功機率是否相等之檢定,
當原來的p-值為妥當p-值時,
改良p-值檢定有一致較高的檢定力,
且為一 $alpha$ 水準檢定.
對於兩獨立二項抽樣母體成功機率勝算比之區間估計,
當原先信賴集合(區間)其真實信賴係數不低於名目水準 $1-alpha$ 時,
由改良p-值檢定所建構的改良信賴集合(區間),
可同時改良集合大小(區間長度)與覆蓋機率,
且保證覆蓋機率至少為 $1-alpha$.
特別在中小樣本情況下,
改良p-值檢定與改良信賴集合(區間)之改進成果更是顯著.
另外,
由貝氏學派的觀點,
分別於兩獨立二項抽樣與多項抽樣下,
使用均勻先驗分布與 Jeffreys 先驗分布推導部分後驗預測p-值,
其數值分析顯示:
當虛無假設成立時,
相較於常用的費雪p-值,
部分後驗預測p-值之分布顯然較接近均勻分布.
摘要(英) The p-value is the most commonly used measure of compatibility of the null model in many applied statistics.
For the statistical inference in discrete data,
the null model often involves the nuisance parameters so that the property of the p-value is more complicated.
This paper considers a procedure which can improve tests used in discrete distributions.
If one constructs a test by a p-value,
the procedure takes such a p-value as a test statistic,
and uses the exact unconditional approach to construct an improved p-value test.
For testing the equality of two independent binomial proportions,
the improved p-value test, which is a level $alpha$ test, is at least as powerful as the original one when the original p-value is valid.
For the interval estimation of the odds ratio in two independent binomial samples,
the improved confidence set (interval) constructed by using the improved p-value test has improvement on interval length and coverage probability
if the original one has coverage probability above the nominal level $1-alpha$.
Also the actual confidence coefficient of the improved confidence set (interval) attains at least 1-$alpha$.
Especially, the improved p-value test and the improved confidence set (interval) significantly outperform the original ones
when the sample sizes are small or moderate.
From Bayesian point of view,
we use the uniform prior and Jeffreys prior to derive the partial posterior predictive p-values
as the data is sampling from the two independent binomial sampling scheme and the multinomial sampling scheme, respectively,
and the numerical studies show that the distribution of the partial posterior predictive p-value
is much closer to the uniform distribution than that of Fisher’’s p-value under the null model.
關鍵字(中) ★ 二項抽樣
★ 正確條件方法
★ 正確非條件方法
★ 改良p-值
★ 信賴區間
★ 貝氏p-值
關鍵字(英) ★ Binomial sampling
★ exact conditional approach
★ exact unconditional approach
★ improved p-value
★ Bayesian p-value
★ confidence interval
論文目次 中文摘要.....i
英文摘要.....ii
誌謝.........iii
目錄.........iv
圖目錄.......vi
表目錄.......vii
第一章 研究動機與文獻回顧.......1
第二章 改良p-值的理論性質.......8
第三章 兩獨立二項抽樣母體成功機率之檢定............13
3.1 簡介................13
3.2 實例研究............19
3.3 檢定大小比較........21
3.4 檢定力比較..........25
第四章 兩獨立二項抽樣成功機率勝算比之區間估計......32
4.1 p-值與信賴區間...........32
4.2 勝算比的正確信賴區間.....36
4.3 實例研究.................43
4.4 區間長度比較.............45
4.5 覆蓋機率比較.............48
第五章 貝氏p-值..............51
5.1 簡介.....................51
5.2 兩獨立二項抽樣之應用.....56
5.3 多項抽樣之應用...........65
第六章 結論..................73
參考文獻.....................79
附錄.........................85
參考文獻 Agresti, A. (1992). A survey of exact inference for contingency tables (with discussion). Statistical Science 7, 131-177.
Agresti, A. (2002). Categorical Data Analysis, 2nd edition. John Wiley & Sons, Hoboken,
New Jersey.
Agresti, A. (2003). Dealing with discreteness: making `exact' confidence intervals for proportions, differences of proportions, and odds ratios more exact. Statistical Methods in Medical Research 12, 3-21.
Agresti, A. and Min, Y. (2001). On small-sample confidence intervals for parameters in discrete distributions. Biometrics 57, 963-971.
Agresti, A. and Min, Y. (2002). Unconditional small-sample confidence intervals for the odds ratio. Biostatistics 3, 379-386.
Agresti, A. and Min, Y. (2005). Simple improved confidence intervals for comparing matched proportions. Statistics in Medicine 24, 729-740.
Barnard, G. A. (1945). A new test for 2X2 tables. Nature 156, 177.
Barnard, G. A. (1947). Significance tests for 2X2 tables. Biometrika 34,
123-138.
Barnard, G. A. (1989). On alleged gains in power from lower p-values. Statistics in medicine 8, 1469-1477.
Barnard, G. A. (1990). Must clinical trials be large? The interpretation of p-values and the combination of test results. Statistics in medicine 9, 601-614.
Bayarri, M. J. and Berger, J. O. (2000). P values for composite null models (with discussion). Journal of the American Statistical Association 95,
1127-1170.
Bayarri, M. J. and Berger, J. O. (2004). The interplay of Bayesian and frequentist analysis. Statistical Science 19, 58-80.
Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd edition. Springer-Verlag, New York.
Berger, J. O. and Delampady, M. (1987). Testing precise hypotheses (with discussion). Statistical Science 2, 317-352.
Berger, J. O. and Wolpert, R. L. (1984). The Likelihood Principle. Institute of
Mathematical Statistics, Hayward, CA.
Berger, R. L. (1996). More powerful tests from confidence interval p-values. The
American Statistician 50, 314-318.
Berger, R. L. and Boos, D. D. (1994). P-values maximized over a confidence set
for the nuisance parameter. Journal of the American Statistical Association 89,
1012-1016.
Berger, R. L. and Sidik, K. (2003). Exact unconditional tests for a 2 2 matched-pairs design. Statistical Methods in Medical Research 12, 91-108.
Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of the Royal Statistical Society Series B 41, 113-147.
Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics: Basic Ideas and Selected Topics. Holden-Day, San Francisco.
Blaker, H. (2000). Confidence curves and improved exact confidence intervals for discrete distributions. The Canadian Journal of Statistics 28, 783-798.
Boschloo, R. D. (1970). Raised conditional level of significance for the 2X2 table when testing the equality of two probabilities. Statistica Neerlandica 24, 1-35.
Box, G. E. P. (1980). Sampling and Bayes inference in scientific modelling and
robustness. Journal of the Royal Statistical Society Series A 143, 383-430.
Casella, G. and Berger, R. L. (2002). Statistical Inference, 2nd edition. Duxbury Press, Pacific Grove, California.
Chen, L. S. and Yang, M. C. (2006). Optimality of the mid p-value for testing
marginal homogeneity in binary matched pairs data. Journal of the Chinese
Statistical Association 44, 33-50.
Clopper, C. J. and Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404-413.
Cornfield, J. (1956). A statistical problem arising from retrospective studies. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (ed. Neyman, J.) 4, 135-148, University of California Press, Berkeley.
Dempster, A. P. (1971). Model searching and estimation in the logic of inference (with discussion). In Foundations of Statistical Inference (V.P. Godambe and D.A. Sprott, eds.) 56-81. Holt, Rinehart and Winston, Toronto.
Dempster, A. P. (1973). The direct use of likelihood for significance testing (with discussion). In Proceedings of Conference on Foundational Questions in Statistical Inference (O. Barndor -Nielsen, P. Blaeslid and G. Schou, eds.)
335-354. Department of Theoretical Statistics, University of Aarhus, Denmark.
Fisher, R. A. (1935). The logic of inductive inference. Journal of the Royal Statistical Society Series A 98, 39-54.
Fries, L. F. et al. (1993). Safety and immunogenicity of a recombinant protein
influenza A vaccine in adult human volunteers and protective efficacy against
wild-type H1N1 virus challenge. Journal of Infectious Diseases 167, 593-601.
Guttman, I. (1967). The use of the concept of a future observation in goodness-of-fit problems. Journal of the Royal Statistical Society Series B 29, 83-100.
Haber, M. (1986). An exact unconditional test for the 2X2 comparative trial. Psychological Bulletin 99, 129-132.
Haber, M (1987). A comparison of some conditional and unconditional exact tests
for 2X2 contingency tables. Communications in Statistics-Simulation and
Computation 16, 999-1013.
Hirji, K. F., Tan, S. J., and Elashoff , R. M. (1991). A quasi-exact test for comparing two binominal proportions. Statistics in Medicine 10, 1137-1153.
Hwang, J. T., Casella, G., Robert, C., Wells, M., and Farrell, R. (1992). Estimation of accuracy of testing. The Annals of Statistics 20, 490-509.
Hwang, J. T. and Pemantle, R. (1997). Estimating the truth indicator function of a statistical hypothesis under a class of proper loss functions. Statistical and Decisions 15, 103-128.
Hwang, J. T. and Yang, M. C. (2001). An optimality theory for mid p-values in 2X2 contingency tables. Statistica Sinica 11, 807-826.
Jeffreys, H. (1967). Theory of Probability, 3rd edition. Oxford University Press, London.
Lancaster, H. O. (1961). Significance tests in discrete distributions. Journal of the American Statistical Association 56, 223-234.
Lehmann, E. L. (1997). Testing statistical hypotheses, 2nd edition. Springer, New York.
Martin Andres, A. and Silva Mato, A. (1994). Choosing the optimal unconditioned
test for comparing two independent proportions. Computational Statistics and
Data Analysis 17, 555-574.
Martin Andres, A., Sanchez Quevedo, M. J., and Silva Mato, A. (1998). Fisher's
mid p-value arrangement in 2X2 comparative trials. Computational Statistics
and Data Analysis 29, 107-115.
McDonald, L. L., Davis, B. M., and Milliken, G. A. (1977). A nonrandomized unconditional test for comparing two proportions in 2 2 contingency tables. Technometrics 19, 145-157.
Mehrotra, D. V., Chan, I. S. F., and Berger, R. L. (2003). A cautionary note on
exact unconditional inference for a difference between two independent binomial
proportions. Biometrics 59, 441-450.
Mendenhall, W. M., Million, R. R., Sharkey, D. E., and Cassisi, N. J. (1984). Stage T3 squamous cell carcinoma of the glottic larynx treated with surgery and/or radiation therapy. International Journal of Radiation Oncology, Biology, Physics 10, 357-363.
Meng, X. L. (1994). Posterior predictive p-values. The Annals of Statistics 22,
1142-1160.
Miettinen, O. and Nurminen, M. (1985). Comparative analysis of two rates. Statistics in Medicine 4, 213-226.
Pearson, k. (1900). On the criterion that a given system of deviations from the
probable in the case of correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine
50, 157-175.
Rohmel, J. (2005). Problems with existing procedures to calculate exact unconditional p-values for non-inferiority/superiority and confidence intervals for two binomials and how to resolve them. Biometrical Journal 47, 37-47.
Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. The Annals of Statistics 12,
1151-1172.
Suissa, S. and Shuster, J. J. (1985). Exact unconditional sample sizes for the 2X2 binominal trial. Journal of the Royal Statistical Society Series A 148,
317-327.
Tang, M. L., Tang, N. S., and Chan, I. S. F. (2005). Confidence interval construction for proportion difference in small-sample paired studies. Statistics in Medicine 24, 3565-3579.
Tocher, K. D. (1950). Extension of the Neyman-Pearson theory of tests to discontinuous variables. Biometrika 37, 130-144.
Troendle, J. F. and Frank, J. (2001). Unbiased confidence intervals for the odds ratio of two independent binomial samples with application to
case-control data. Biometrics 57, 484-489.
Upton, G. J. G. (1992). Fisher's exact test. Journal of the Royal Statistical Society Series A 155, 395-402.
Yang, M. C., Lee, D. W., and Hwang, J. T. (2004). The equivalence of the mid
p-value and expected p-value for testing equality of two balanced binomial proportions. Journal of Statistical Planning and Inference 126, 273-280.
Yates, F. (1984). Test of significance for 2X2 contingency tables. Journal of the Royal Statistical Society Series A 147, 426-463.
指導教授 楊明宗(Ming-Chung Yang) 審核日期 2006-6-20
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明