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| 研究生： |
曾能芳 Chan, Lan Fun |
|---|---|
| 論文名稱： |
The Box-Cox 依變數轉換之技巧 The Box-Cox Transformation: A Review |
| 指導教授： | 鄭天澤 |
| 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： | 1996 |
| 畢業學年度： | 84 |
| 語文別： | 英文 |
| 論文頁數： | 43 |
| 中文關鍵詞： | 強力轉換 、常態化轉換 、架構變數 、分數檢定 、敏感性 |
| 外文關鍵詞： | power transformation, normalized transformation, constructed variable, scores test, Andrews's exact test, sensitivity |
| 相關次數： | 點閱：279 下載：0 |
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The use of transformation can usually simplify the analysis of data, especiallywhen the original observations deviate from the underlying assumption of linearmodel. Box-Cox transformation receives much more attention than others. Inthis dissertation, we will review the theory about the estimation, hypotheses test on transformation parameter and about the sensitivity of the linear model parameters. Monte Carlo simulation is used to study the performance of the transformation. We also display whether Box-Cox transformation makes the transformed observations satisfy the assumption of linear model actually.
謝辭
Abstract
CONTENTS
Chapter 1 INTRODUCTION-----1
Chapter 2 POWER TRANSFORMATION-----3
2.1 Estimation of λ-----3
2.1.1 Box-Cox method-----3
2.1.2 Atkinson's method-----4
2.2 Asymptotic properties of λ, θ(λ) and σ(λ)-----6
2.3 Hypotheses tests about λ-----6
2.3.1 Likelihood ratio test-----7t
2.3.2 The scores test-----7
2.3.3 Andrews's test-----8
2.4 Randomness of λ-----9
2.4.1 λ regarded as random-----10
2.4.2 λ regarded as fixed-----12
Chapter 3 SENSITIVITY FOR LINEAR MODEL PARAMETER-----14
3.1 Stability for contrast parameter-----15
3.2 Sensitivity for location parameter-----17
3.3 Simulation-----19
Chapter 4 TRANSFORMATION TO SYMMETRY-----25
4.1 Skewness of y<sub>i</sub><sup>(λ)</sup> with non-normal distribution-----25
4.2 Precision of the normal-theory estimate λ<sub>N</sub>-----26
4.3 Estimate of new λ to symmetry-----27
Chapter 5 CONCLUSION-----30
APPENDIX A Asymptotic maximum likelihood theory-----32
APPENDIX B Normal-theory maximum likelihood-----34
REFERENCE-----35
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