母體平均值比較的一致強韌分數統計量

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：8

、訪客IP：52.14.221.113

姓名

劉小篔(Hsiao-yun Liu) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

母體平均值比較的一致強韌分數統計量
(A unified robust score statistic for population means comparison)

相關論文

★ 不需常態假設與不受離群值影響的選擇迴歸模型的方法	★ 用卜瓦松與負二項分配建構非負連續隨機變數平均數之概似函數
★ 強韌變異數分析	★ 用強韌概似函數分析具相關性之二分法資料
★ 利用Bartlett第二等式來估計有序資料的相關性	★ 相關性連續與個數資料之強韌概似分析
★ 不偏估計函數之有效性比較	★ 一個分析相關性資料的新方法-複合估計方程式
★ (一)加權概似函數之強韌性探討 (二)影響代謝症候群短期發生及消失的相關危險因子探討	★ 利用 Bartlett 第二等式來推論模型假設錯誤下的變異數函數
★ (一)零過多的個數資料之變異數函數的強韌推論 (二)影響糖尿病、高血壓短期發生的相關危險因子探討	★ 一個分析具相關性的連續與比例資料的簡單且強韌的方法
★ 時間數列模型之統計推論	★ 複合概似函數有效性之探討
★ 決定分析相關性資料時統計檢定力與樣本數的普世強韌法	★ 檢定DNA鹼基替換模型的新方法 - 考慮不同DNA鹼基間的相關性

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]

至系統瀏覽論文 ( 永不開放)

摘要(中)

在母體分配未知的情形下，本文處理母體平均值的比較問題，探討的問題與變異數分析(analysis of variance)法類似，但我們不做母體分配的假設。
我們藉由修正包括珈瑪、常態、卜阿松、負二項及逆高斯模型的分數統計量，導出這個強韌檢定統計量，這個統計量有熟悉的(觀察值-期望值)的型式。儘管這些分配不同，但產生唯一且一致的強韌分數統計量，且此強韌分數統計量可以推廣至指數族的分配。同時，我們提出強韌檢定優於目前其他的檢定方法的條件，並證明這些性質。再經由模擬和實際資料分析，我們呈現強韌分數檢定有限樣本的性質。

摘要(英)

This dissertation deals with comparison of population means, similar to that of analysis of variance, in a way that the knowledge of the underlying distributions is absent. We develop a novel robust score test statistic that is akin to the familiar (observed-expected)/expected formula, with extra terms incorporating impact of the unspecified population moments.
We derive the test by correcting the score statistics from models including gamma, normal, Poisson, negative-binomial and inverse-Gaussian. These models, in spite of their diversity, give rise to a single unified corrected robust score statistic which can be extended to exponential family distributions. Conditions under which our new robust test is more powerful than current competitors are provided. Finite sample performance is demonstrated via simulations and real data analysis.

關鍵字(中)

★ 強韌分數統計量
★ 變異數分析
★ 指數族的分配

關鍵字(英)

★ Robust score statistic
★ Analysis of variance
★ Exponential family distribution

論文目次

摘要……………………………………………………….…………………………....... i
Abstract…………………………………………………………………………………..... ii
致謝辭…………………………………………………………………………………....... iii
Contents…………………………………………………………………………………… v
Chapter 1 Introduction…………………………………………………………………… 1
Chapter 2 Unified test for population means comparison….…………………..…........ 3
2.1 Exponential families as working models…………………………………………… 5
2.1.1 Testing …………………………………………………
6
2.1.2 Testing ………………………………………………..
11
2.2 Five working model distributions…………………………………………………... 15
2.2.1 Gamma distribution working model…………………………………………… 15
2.2.2 Normal distribution working model………………………………………….... 20
2.2.3 Negative-binomial distribution working model……………………………….. 25
2.2.4 Poisson distribution working model…………………………………………… 29
2.2.5 Inverse-Gaussian distribution working model………………………………..... 34
2.3 A unified robust score test…………………………………………………………... 39
2.4 Three groups comparison of and ……………………………………………...
44
Chapter 3 Simulation studies………...…………………………………………………... 46
3.1 Comparisons of means for two groups……………………………….…………….. 46
3.2 Comparisons of means for three groups…………………………………………..... 47
3.3 Comparisons of means for four groups……………………………………………... 48
3.4 The size and power of the four test statistics……………………………………….. 48
Tables……………………………………………………………………………………..... 50
Chapter 4 Real examples………………………………………………...……………….. 86
Chapter 5 Conclusions…………………………………………………………………..... 98
References……………………………………………………….………………………… 99
Appendix A………………………………………………………………………………... 101
Appendix B………………………………………………………………………………... 104

參考文獻

Barnwal, R. K. and Paul, S. R. (1988). Analysis of one-way layout of count data with negative binomial variation. Biometrika 75, 215-222.
Bartlett, M.S. (1953). Approximate confidence intervals. Biometrika 40, 12–19.
Cox, D. R. and Hinkley, D. V. (1974).Theoretical Statistics, Chapman and Hall.
Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference. JRSS-B 49, 1-39.
Faddy, M. J. and Bosch, R. J. (2001) Likelihood-based modeling and analysis of data underdispersed relative to the Poisson distribution. Biometrics 57, 620-624.
Jones, James. (2016). Introduction to applied statistics: Lecture notes, courses taught Math 113, richland community college.
Kish, L. (1965). Survey Sampling. Wiley, New York.
Michelson, A. A.and Morley, E. W. (1887) American Journal of Science 34, 333–345..
Neyman, J. (1959). Optimal asymptotic tests of composite hypotheses. In: Grenander,
U. (Ed.), Probability and Statistics. Wiley, New York, pp. 213-234.
Rao, J. N. K. and Scott, A. J. (1999). A simple method for analyzing overdispersion in clustered Poisson data. Statistics in Medicine 18, 1373-1385.
Royall, R. M. and Tsou, T-S. (2003). Interpreting statistical evidence using imperfect models: Robust adjusted likelihood functions. JRSS-B 65, 391-404.
Saha, K. K. (2008). Analysis of one-way layout of count data in the presence of over or under dispersion. Journal of Statistical planning and inference 138, 2067-2081.
Saha, K. K. (2009). Testing the homogeneity of the means of several groups of count data in the presence of unequal dispersions. Computational Statistics and Data Analysis 53, 3305-3313
Snedecor , George W. (1956). Statistical Methods: fifth edition. Iowa State college press, Ames.
Tsou, T-S and Chen, C-H. (2008). Comparing means of several dependent populations
of count-a parametric robust approach. Statistics in Medicine 27, 2576-2585.
Tsou, T-S. (2009). Performing legitimate parametric regression analysis without knowing the true underlying random mechanisms. Communications in Statistics - Theory and Methods 38, 1680-1689.
Weeks, A. J. (1983), A Genstat Primer. Arnold, London.

指導教授

鄒宗山(Tsung-Shan Tsou)

審核日期

2016-7-18

推文