[1]徐伟娟.2×2表参数置信域的几何方法[J].东南大学学报(自然科学版),2005,35(4):645-649.[doi:10.3969/j.issn.1001-0505.2005.04.033]
 Xu Weijuan.Geometry method of confidence interval on 2× 2 table[J].Journal of Southeast University (Natural Science Edition),2005,35(4):645-649.[doi:10.3969/j.issn.1001-0505.2005.04.033]
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2×2表参数置信域的几何方法()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
35
期数:
2005年第4期
页码:
645-649
栏目:
数学、物理学、力学
出版日期:
2005-07-20

文章信息/Info

Title:
Geometry method of confidence interval on 2× 2 table
作者:
徐伟娟
东南大学数学系, 南京 210096
Author(s):
Xu Weijuan
Department of Mathematics, Southeast University, Nanjing 210096, China
关键词:
简单差 危险率 置信区间 非线性多项分布模型
Keywords:
simple difference risk ratio confidence interval multinomial nonlinear model
分类号:
O211.9
DOI:
10.3969/j.issn.1001-0505.2005.04.033
摘要:
对于生物医学统计中的一类二次感染问题,提出了一种研究其简单差和危险率的区间估计几何方法.比较系统地研究了非线性多项分布模型参数置信域的几何理论,通过基于曲率的置信域和基于Score检验的置信域这2种方法得到了3个关于参数置信域的定理.抽象出二次感染问题为一个特殊的非线性多项分布(三项分布)模型,其概率密度为:p(Y; π(θ))=n!∏3i=1yii(θ)/yi!),其中Y={y1,y2,y3}T,∑3i=1πi(θ)=1, ∑3i=1yi=n,并进一步指出这些定理对于2×2表以及二次感染问题的应用.
Abstract:
A geometry method is brought forward in this article to analyze the interval estimate of the simple difference(SD)and risk ratio(RR)between the proportions of the primary infection and the secondary infection in biomedical statistics. A geometry theory of multinomial nonlinear models is also analyzed systematically study and three theorems about confidence interval of parameter are proved. The secondary infection given the primary infection is regarded as a special multinomial nonlinear model as follows: p(Y; π(θ))=n!∏3i=1yii(θ)/yi!),Y={y1,y2,y3}T,∑3i=1πi(θ)=1,∑3i=1yi=n. And the three theorems proved above are applied to the 2×2 table and the secondary infection given the primary infection and the primary infection.

参考文献/References:

[1] Agresti A.Categorical data analysis [M].New York:Wiley,1990.45-46.
[2] Beal S L.Asymptotic confidence intervals for the difference between two binomial parameters for use with small sample [J]. Biometrics,1987,43:941-950.
[3] Chan I S F,Zhang Z-X.Test-based exact confidence intervals for the differences of two binomial proportions [J]. Biometrics,1999,55:1202-1209.
[4] Tango T.Equivalence test and confidence interval for the difference in proportions for the paired-sample design [J].Statistics in Medicine,1998,17:891-908.
  [5] Lui K-J.Interval estimation of risk ratio between the secondary infection given the primary infection and the primary infection [J]. Biometrics,1998,54(2):706-711.
[6] Lui K-J.Confidence intervals of the simple difference between the proportions of a primary infection and a secondary infection,given the primary infection [J].Biometrical Journal,2000,42(1):59-69.
[7] Wei B C.Geometry of multinomial distribution models [J].Advances in Mathematics,1993,22(1):84-85.
[8] Bates D M,Watts D G.Relative curvature measures of nonlinearity [J]. J R Statiis Soc Ser B,1980,42(1):1-25.
[9] 韦博成.现代非线性回归分析 [M].南京:东南大学出版社,1989.1-2.
[10] Wei B-C.Exponential family nonlinear models[M].Berlin:Springer Germany,1998.31-53.
[11] Wei B-C.Some asymptotic inference in multinomial nonlinear models [J]. Appl Math JCU,1996,11(B):273-284.
[12] Hamilton D C.Confidence regions for parameter subsets in nonlinear regression [J].Biometrika,1986,73(1):57-64.

备注/Memo

备注/Memo:
作者简介: 徐伟娟(1977—),女,硕士.
更新日期/Last Update: 2005-07-20