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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宏(Hung Chen) | |
| dc.contributor.author | Rei-Yang Wang | en |
| dc.contributor.author | 王瑞陽 | zh_TW |
| dc.date.accessioned | 2021-06-08T05:20:27Z | - |
| dc.date.copyright | 2011-08-03 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-29 | |
| dc.identifier.citation | [1] Ahn, M. (2010). Random E ect Selection in Linear Mixed Models.
North Carolina State University Ph.D. dissertation. Permanent URL: http://gradworks.umi.com/34/42/3442585.html. [2] Akaike, H. (1973). Maximum likelihood identi cation of gaussian autoregressive moving average models. Biometrika, 60, 255-265. [3] Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B 57, 289-300. [4] Casella, G. and Berger, R.L. (1991). Statistical Inference, Duxbury Press, New York. [5] Chen, K. and Wang, J.L. (2010). Identifying Di erentially Expressed Genes for Time-course Microarray Data through Functional Data Analysis. Statistics in Biosciences, 2, 95-119. [6] Efron, B. (1986). How Biased is the Apparent Error Rate of a Prediction Rule? Biometrika, 81, 461-470. [7] Geert, V. and Geert, M. (2000). Linear Mixed models for Longitudinal Data, Springer-Verlag, NewYork. [8] Harville, D.A. (1976). Extension of the Gauss-Markov Theorem to In- clude the Estimation of Random E ects. Annals of Statistics, 4, 384-395. [9] Harville, D.A. (1977). Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems. Journal of the American Statistical Association, 72, 320-338. [10] Hartley, H.O. and Rao, J.N.K. (1976). Maximum-likelihood estimation for the mixed analysis of variance model. Biometrika, 54, 93-108. [11] Jiang, J., Rao, J.S., Gu, Z., and Nguyen, T. (2008). Fence methods for mixed model selection. The Annals of Statistics, 36, 1669-1692. [12] Laird, N.M. and Ware, J.H. (1982). Random-E ects Models for longitudinal Data. Biometrics, 38, 963-974. [13] Mallows, C.L. (1973). Some Comments on CP. Technometrics 15, 661-675. [14] Millar, J.J. (1977). Asymptotic Properties of maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance. Annals of Statistics, 5, 746-762. [15] Ramsay, J.O. and Silverman, B.W. (1997).Functional Data Analysis, Springer-Verlag, NewYork. [16] Ramsay, J.O. and Silverman, B.W. (2002).Applied Functional Data Analysis: Methods and Case Studies, Springer-Verlag, NewYork. [17] Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461-464. [18] Wang, J. and Kim, S.K. (2003). Global Analysis of dauer gene expression in Caenorhabditis elegans. Development, 130, 1621-1634. [19] Zhang, B. (2009). Adaptive model selection in linear mixed models. University of Minnesota Ph.D. dissertation. Permanent URL:http://purl.umn.edu/56303. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/24275 | - |
| dc.description.abstract | 模型選擇在統計上是一個在一群候選模型中選擇最佳模型的過程。適合度則決定了模型配適資料的好壞程度。我們一般會以增加模型中參數個數，意即模型複雜度，來提昇資料適合度，然而由於雜訊的干擾，對於他組資料的適合度則有所限制。如何在模型複雜度及資料適合度間取得平衡，已經在許多文獻中有所討論。文獻中已經發現在線性迴歸中，Cp統計量可用於選擇合理模型。
這篇論文是由Chen and Wang (2010)所啟發，該論文透過每個基因的函數型資料型態中的隨機係數及潛在變項來區分出差異表現量基因。在該研究中，他們分別使用在控制組及實驗組中隨著時間改變的基因表現比較。在這樣的設計下，他們的模型可以視為一個包含隨機效應的二因子變異數分析。在這篇論文中，我們嘗試推導包含隨機效應的二因子變異數分析的Cp統計量，以探討如何在變異數分析模型中選擇隨機效應因子。透過固定及隨機效應模型中預測風險的比較，可以發現Cp統計量可用來分辨隨機效應。在此篇論文中將會討論一些特定模型形式。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-08T05:20:27Z (GMT). No. of bitstreams: 1 ntu-100-R98221033-1.pdf: 575756 bytes, checksum: 03a423d6c5d66e0654a249f49a91bee0 (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 誌謝 i
中文摘要 ii Abstract iii Content iv 1 Introduction 1 2 Motivated Data Set 4 2.1 A Brief Summary of Chen and Wang (2010) 4 2.2 Model development 5 2.2.1 Time-course experiment 5 2.2.2 The Karhunen-Loeve representation 6 2.2.3 Model Construction for Detecting Dierential Gene Expression in treatment-Control Time Course 8 2.2.4 Decomposition of the Random Coefficients 9 2.2.5 Variance Parameter Estimation 9 2.2.6 EM algorithm and multiple testing 10 2.3 Connection with linear mixed effect model 12 3 Linear mixed-effect models 14 4 Prediction error on ANOVA with random effects 16 4.1 Prediction risk of one-way xed eect ANOVA 16 4.2 Prediction risk of random effect model in over-fi tted case 19 4.3 Prediction risk of random effect model in under fitted case 20 4.4 Two-way ANOVA with random effects 21 5 Discussion 25 6 Appendix 27 6.1 Estimation of y in random effect model 27 6.2 Trace of V^(-1) 27 | |
| dc.language.iso | en | |
| dc.title | 平衡資料結構下隨機效應變異數分析模型之無偏風險估計 | zh_TW |
| dc.title | On Unbiased Risk Estimation of Random Effect ANOVA Model with Balanced Data | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 江金倉,陳素雲,蕭朱杏 | |
| dc.subject.keyword | 無偏風險估計,隨機效應, | zh_TW |
| dc.subject.keyword | Unbiased Risk Estimation,Random Effect, | en |
| dc.relation.page | 30 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2011-07-29 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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