Please use this identifier to cite or link to this item:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30532Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 陳宏 | |
| dc.contributor.author | Huey-Fan Ni | en |
| dc.contributor.author | 倪惠芬 | zh_TW |
| dc.date.accessioned | 2021-06-13T02:07:21Z | - |
| dc.date.available | 2009-07-12 | |
| dc.date.copyright | 2007-07-12 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-03 | |
| dc.identifier.citation | [1] Bose, R. C. (1947). The design of experiments. Proc. Indian Sci. Congr., 34(II), 1-25.
[2] Birkes, D., Dodge, Y. and Seely, J. (1976). Spanning sets for estimable contrasts in classification models. Ann. Statist., 4, 86-107. [3] Callows, M. J., Dudoit, S., Gong, E. L., Speed, T. P. and Rubin, E. M. (2000). Microarray expression profiling identifies genes with altered expression in HDL-deficient mice. Genome Res., 10, 2022-2029. [4] Chakrabarti, M. C. (1963). On the C-matrix in design of experiments. J. Ind. Statist. Assoc., 1, 8-23. [5] Chen, Y., Dougherty, E. R. and Bittner, M. L. (1997). Ratio-based decisions and the quantitative analysis of cDNA microarray image. J. Biomed. Optics., 2, 364-374. [6] Dodge, Y. ( 1985). Analysis of experiments with missing data. New York Wiley. [7] Dudoit, S., Yang, Y. H., Luu, P., Lin, D. M., Peng, V., Ngai, J. and Speed, T. P. (2002a). Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation. Nucleic Acids Research, 30, e15. [8] Dudoit, S., Yang, Y. H., Speed, T. P. and Callows, M. J. (2002b). Statistical methods for identifying differentially expressed genes in replicated cDNA Microarray Experiments. Statistica Sinica, 12, 111-139. [9] Eccleston, J. A. and Russell, K. (1975). Connectedness and orthogonality in multifactor designs. Biometrika, 62, 341-345. [10] Fan, J., Tam, P., Vande Woude, G. and Ren, Y. (2004). Normalization and analysis of cDNA micro-arrays using within-array replications applied to neuroblastoma cell response to a cytokine. Proceedings of the National Academy of Science., 101, 1135-1140. [11] Fan, J., Huang, T. and Peng, H. (2005). Semilinear high-dimensional model for normalization of microarray data: a theoretical analysis and partial consistency. (with discussion) J. Amer. Statist. Assoc., 100, 781-813. [12] Godolphin, J. D. (2004). Simple pilot procedures for the avoidance of disconnected experimental designs. Appl. Statist., 53, 133-147. [13] Heiligers, B. (1991). A note on connectedness of block designs. Metrika, 38, 377-381. [14] Huang, J., Wang, D. and Zhang, C. (2005). A two-way semi-linear model for normalization and analysis of cDNA microarray data. J. Amer. Statist. Assoc., 100, 814-829. [15] Huang, J. and Zhang, C. H. (2005). Asymptotic analysis of a two-way semiparametric regression model for microarray data. Statistica Sinica, 15, 597-618. [16] Kerr, M. K., Martin, M. and Churchill, G. A. (2000). Analysis of variance for gene expression microarray data. J. Comput. Biol., 7, 819-837. [17] Park, D. K. and Shah, K. R. (1995). On connectedness of row-column designs. Comm. Statis. Theory Methods, 24(1), 87-96. [18] Searle, S. R. (1987). Linear Models for Unbalanced Data. Wiley, New York. [19] Shah, K. R. and Sinha, B. K. (1996). Row-column designs. In: Ghosh and Rao, eds., Linear Models for Unbalanced Data. Vol 13, 903-937, Wiley, New York. [20] Stone, C. J. (1975). Nearest neighbor estimators of a nonlinear regressionfunction. Proc. Computer Sci. Statist. 8th Ann. Symp. Interface, 413-418, Health Sciences Computer Facility, UCLA. [21] Stone, C. J. (1977). Consistent nonparametric regression (with discussion). Ann. Statist., 5, 549-645. [22] Stone, C. J. (1982). Optimal global rates of convergence for nonparametric regression. Ann. Statist., 10, 1040-1053. [23] Stone, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist., 13, 689-705. [24] Neyman, J. and Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometricka, 16, 1-32. [25] Yang, Y. H. and Speed, T. (2002). Design issues for cDNA microarray experiments. Nature Reviews Genetics, 3(8):579-588. [26] Weeks, D. L. and Williams, D. R. (1964). A note on the determination of connectedness in an N-way cross classification. Technometrics, 6, 319-324. Errata, Technometrics, 7, 281, 1965. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30532 | - |
| dc.description.abstract | 這個研究的動機來自於將微陣列實驗(microarray experiment)所得到之基因表現值正規化(normalization), 我們考慮具有基因與區塊(block)二個因子(factor)的實驗. 由於每個基因複製(replication)的次數遠小於區塊的個數, 所以我們考慮的二因子實驗為不完整的(incomplete). 當對由微陣列實驗所產生的資料配適(fit)具相加性的二方式分類模型(additive two-way classification model), 是否所有由未之參數所形成的對比(contrast)皆為可估(estimable)是一個值得討論的問題.
假設第i個因子為不完整的N-因子實驗中主要感興趣的因子. 當對由實驗所產生的資料配適具相加性的N-方式分類模型, 我們討論消去與其他因子有關的未知參數(unknown parameter)所獲得之縮小的正規方程(reduced normal equation)的係數矩陣(coefficient matrix)之結構. 然後, 以此係數矩陣之分解為起點, 我們提出一個演算法使得具相加性的N-方式分類模型中的有效參數(effective parameter)可以被確認. 針對具相加性的二方式分類模型, 我們提出得到具一致性(consistency)之未知參數估計的充分且必要條件(sufficient and necessary condition). 最後, 我們以每一個格子(cell)至少具有一個觀查值的行列設計(row-column design)與一組由微陣列實驗所產生的資料來闡明研究中所提出之係數矩陣的分解與演算法. | zh_TW |
| dc.description.abstract | Motivated by 'local normalization' to remove bias in the measured gene expressions of microarray experiments, we consider the two-factor experiment with the factors gene and block. Since the number of replications of each gene is much smaller than the number of blocks, the considered two-factor experiment is incomplete. As an additive two-way classification model is fitted to the microarray data, whether all contrasts formed by unknown parameter are estimable has to be discussed.
Suppose that the ith factor of the incomplete N-factor experiment is the factor of interest. As an additive N-way classification model is fitted to the data, the structure of the coefficient matrix of reduced normal equation obtained by eliminating the parameters of the other factors is discussed. Then, an algorithm is proposed to identify the effective parameters in an additive N-way classification model based on the proposed decomposition of the coefficient matrix. A necessary and sufficient condition for getting consistent estimates of unknown parameters in an additive two-way classification model is provided. The new decomposition and algorithm are illustrated by a row-column design with at least one observation per cell and 'normalization' for microarray data in which the pin and dye bias are considered to be corrected. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T02:07:21Z (GMT). No. of bitstreams: 1 ntu-96-D92842007-1.pdf: 2691261 bytes, checksum: 1b92850fd71fcd661fe5a64a90273708 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | 中文摘要 ii
英文摘要 iii 1 Introduction 1 1.1 Normalization for Microarray Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.3 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Literature Review 6 2.1 Two Semiparametric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Convergence for Nonparametric Regression Estimation . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Nonparametric Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 An Additive Approximation to f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Connectedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 3 Preliminaries 15 3.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 3.1.1 The Additive Two-way Classification Model . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2 The Additive N-way Classification Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 3.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.1 Least-squared Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 3.2.2 Interpretation of the Estimating Procedure when . . . . . . . . . . . . . . . . . .22 3.3 A Novel Decomposition of the C-matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.1 Structure of the C-matrix when N = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.2 Determination of the Effective Parameters when N = 2 . . . . . . . . . . . . . . . . . . .25 3.3.3 Structure of the C-matrix when N > 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 3.3.4 Determination of the Effective Parameters when N > 2 . . . . . . . . . . . . . . . . . . 37 4 Large Sample Properties 41 4.1 The Variance and Covariance of the Estimators . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2 Consistent Property of the Estimators under the Unstructured Design . . . . . . . 44 4.3 Consistent Property of the Estimators under the Structured Design . . . . . . . . . . .47 5 Algorithms to Determine Effective Parameters 49 5.1 The Algorithm to Determine the Effective Parameters when N = 2 . . . . . . . . . . .49 5.2 The Algorithm to Determine the Effective Parameters when N > 2 . . . . . . . . . . .51 5.3 The Suggestion to Produce a Connected Design . . . . . . . . . . . . . . . . . . . . . . . . . 54 6 Illustration 56 6.1 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 6.1.1 Empirically Illustration of the Proposed Decomposition of the C-matrix . . . . .56 6.1.2 Empirically Illustration of the Proposed Algorithm in Section 5.1 . . . . . . . . .58 6.1.3 Consistent Property of the Estimators when the Data is Unbalanced . . . . . . . . 60 6.1.4 Empirically Illustration of the Proposed Algorithm in Section 5.2 . . . . . . . . .63 6.2 Analysis of the Microarray Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 7 Conclusion and Discussion 72 A The Estimability of Parameters in ANOVA Model II 75 B Proof of Lemma 1 79 C Proof of Theorem 2 81 D Proof of Theorem 3 85 E Proof of large sample properties of estimators 86 E.1 Proof of Theorem 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 E.2 Proof of Lemma 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 E.3 Proof of Theorem 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88 E.4 Proof of Theorem 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88 E.5 Proof of Theorem 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88 E.6 Proof of Theorem 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89 F Proof of Lemma 3 92 Biliography 93 | |
| dc.language.iso | en | |
| dc.subject | 連接性 | zh_TW |
| dc.subject | 有效的參數 | zh_TW |
| dc.subject | 對比 | zh_TW |
| dc.subject | 可估計 | zh_TW |
| dc.subject | 分類模型 | zh_TW |
| dc.subject | 一致估計 | zh_TW |
| dc.subject | 不完整的N-因子實驗 | zh_TW |
| dc.subject | 行列設計 | zh_TW |
| dc.subject | consistent estimator | en |
| dc.subject | connectedness | en |
| dc.subject | effective parameter | en |
| dc.subject | contrast | en |
| dc.subject | estimable | en |
| dc.subject | Classification model | en |
| dc.subject | row-column design | en |
| dc.subject | incomplete N-factor experiment | en |
| dc.title | 具相加性的無母數迴歸模式在一般性設計中的估計問題 | zh_TW |
| dc.title | Estimation Problem in Nonparametric Additive Regression Model under General Design | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.coadvisor | 戴政 | |
| dc.contributor.oralexamcommittee | 張淑惠,陳秀熙,蔡風順,鄭光甫 | |
| dc.subject.keyword | 分類模型,可估計,對比,有效的參數,連接性,不完整的N-因子實驗,行列設計,一致估計, | zh_TW |
| dc.subject.keyword | Classification model,estimable,contrast,effective parameter,connectedness,incomplete N-factor experiment,row-column design,consistent estimator, | en |
| dc.relation.page | 95 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-03 | |
| dc.contributor.author-college | 公共衛生學院 | zh_TW |
| dc.contributor.author-dept | 流行病學研究所 | zh_TW |
| Appears in Collections: | 流行病學與預防醫學研究所 | |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| ntu-96-1.pdf Restricted Access | 2.63 MB | Adobe PDF |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.