非穩定空間相關函數的懲罰概似估計

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陳穎頻(Yin-Ping Chen) 查詢紙本館藏

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論文名稱

非穩定空間相關函數的懲罰概似估計
(Nonstationary Spatial Covariance Estimation Using Penalized Likelihood)

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摘要(中)

本論文主要研究經驗正交函數(empirical orthogonal functions)對非穩定空間相關函數的估計問題，我們假設資料在空間中不同的時間點重複蒐集，但採樣的地點可能是稀少、不規則分佈的。針對這樣的問題目前有兩種處理方法，一種方法是將空間隨機過程局限在一組給定函數所展開的空間中，另一種方法則先在密集格點上內插資料，再利用主成分分析法獲得經驗正交函數的估計。有別於這兩種方法，本論文提出兩個半母數空間模型，結合平滑樣條函數(smoothing splines)或迴歸樣條函數(regression splines)，以最大懲罰概似函數法，直接得到經驗正交函數的估計。我們以期望條件最大演算法(expectation conditional maximization algorithm)，同時獲得所有模型參數的估計值。模擬結果顯示我們所提出的方法無論對於平穩或是非平穩的空間隨機過程，其空間相關函數估計或空間預測準確度皆有良好的表現。此外我們也將所發展的方法應用於分析美國科羅拉多州的雨量資料，並進一步將空間模型擴展至時空模型，用以分析同時具有時間及空間相關性的資料。

摘要(英)

This thesis considers nonstationary spatial covariance estimation using empirical orthogonal functions (EOFs) under the consideration that data may be observed only at some sparse, irregularly spaced locations with repeated measurements. Instead of obtaining EOFs by principal component analysis based on a class of pre-specified basis functions or a pre-smoothing step with data imputed on a regular grid, two semiparametric approaches are advocated for EOF estimation, which are based on smoothing splines and regression splines using penalized likelihood. An expectation-conditional-maximization algorithm is proposed to obtain the penalized maximum likelihood estimates of the mean and the covariance parameters simultaneously. Some simulation results show that the proposed methods perform well in both spatial prediction and covariance function estimation, regardless of whether the underlying spatial process is stationary or nonstationary. In addition, the methods are applied to analyze a precipitation dataset in Colorado. Some further extension to spatio-temporal models is also provided.

關鍵字(中)

★ 期望條件最大演算法
★ 經驗正交函數
★ 非平穩空間相關函數
★ 懲罰概似
★ 懲罰迴歸樣條函數
★ 平滑樣條函數
★ 空間預測
★ 時空模型

關鍵字(英)

★ ECM algorithm
★ empirical orthogonal function
★ nonstationary spatial covariance model
★ penalized likelihood
★ penalized regression splines
★ smoothing splines
★ spatial prediction
★ spatio-temporal modeling

論文目次

1 Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Nonstationary Geostatistical Models . . . . . . . . . . . . . . . . . . . . . . . 2
2 Geostatistical Models 5
2.1 Stationary Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Nonstationary Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Moving-Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 Nonstationary Matérn Covariance . . . . . . . . . . . . . . . . . . . . 9
2.2.5 Weighted Stationary Processes . . . . . . . . . . . . . . . . . . . . . . 9
2.2.6 Empirical Orthogonal Function Analysis . . . . . . . . . . . . . . . . 10
2.3 Spatial Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Splines 18
3.1 Smoothing Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Regression Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 EOF Estimation by Smoothing Splines 22
4.1 The Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1.1 Penalized Maximum Likelihood . . . . . . . . . . . . . . . . . . . . . 23
4.1.2 Spatial Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 A Multicycle ECM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 A Spatio-Temporal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4.1 Experiment I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4.2 Experiment II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4.3 Experiment III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.4.4 Experiment IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4.5 Experiment V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 EOF Estimation by Penalized Regression Splines 48
5.1 The Proposed Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2 A Multicycle ECM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.3 A Spatio-Temporal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4.1 Experiment VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.4.2 Experiment VII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.4.3 Experiment VIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6 A Real Data Example 58
7 Discussion and Further Research 63
7.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.2 Further Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.2.1 Selection via Regularization . . . . . . . . . . . . . . . . . . . . . . . 64
7.2.2 Spatio-Temporal Models . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.2.3 Asymptotic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 65
References 66
Appendix 75

參考文獻

1. Abrahamsen, P. (1992), “Bayesian kriging for seismic depth conversion of a multi-layer reservoir,” Geostatistics Tróia ’92, edited by A. Soares, Kluwer, Dordrecht, 385-398.
2. Albert, P. S. and McShane, L. M. (1995), “A generalized estimating equations approach for spatially correlated binary data: Applications to the analysis of neuroimaging data,” Biometrics, 51, 627-638.
3. Alishouse, J. C., Crone, L. J., Fleming, H. E., Van Cleef, F. L., and Wark, D. Q. (1967), “A discussion of empirical orthogonal functions and their application to vertical temperature profiles,” Tellus, 19, 477-482.
4. Anderes, E. B. and Stein, M. L. (2008), “Estimating deformations of isotropic Gaussian random fields on the plane,” Annals of Statistics, 36, 719-741.
5. Anderes, E. B. and Stein, M. L. (2011), “Local likelihood estimation for nonstationary random fields,” Journal of Multivariate Analysis, 102, 506-520.
6. Armstrong, M., and Delfiner, P. (1980), “Towards a more robust variogram: A case study on coal,” Technical Report N-671, Centre de Geostatistique, Fontainebleau, France.
7. Armstrong, M., and Jabin R. (1981), “Variogram models must be positive-definite,” Journal of the International Association for Mathematical Geology, 13, 455-459.
8. Braud, I., Obled, Ch., and Phamdinhtuan, A. (1993), “Empirical Orthogonal Function (EOF) analysis of spatial random fields: Theory, accuracy of the numerical approximations and sampling effects,” Stochastic Hydrology and Hydraulics, 7, 146-160.
9. Brown, P. J. and Zidek, J. V. (1980), “Adaptive multivariate ridge regression,” The Annals of Statistics, 8, 64-74.
10. Buell, C. E. (1972), “Integral equation representation for factor analysis,” Journal of the Atmospheric Sciences, 28, 1502-1505.
11. Chilès, J. P. and Delfiner P. (2012), Geostatistics: Modeling Spatial Uncertainty, 2nd ed., Wiley, New York.
12. Claeskens, G., Krivobokova, T., and Opsomer, J. (2009), “Asymptotic properties of penalized spline estimators,” Biometrika, 96, 529-544.
13. Clerc, M. and Mallat, S. (2003), “Estimating deformations of stationary processes,” Annals of Statistics, 31, 1772-1821.
14. Cleveland, W. S. (1979), “Robust locally weighted regression and smoothing scatter plots,” Journal of the American Statistical Association, 74, 829-836.
15. Cleveland, W. S. and Devlin, S. J. (1988), “Locally-weighted regression: an approach to regression analysis by local fitting,” Journal of the American Statistical Association, 83, 596-610.
16. Cohen, A. and Jones, R. H. (1969), “Regression on a random field,” Journal of the American Statistical Association, 64, 1172-1182.
17. Cressie, N. (1993), Statistics for Spatial Data, revised edition, Wiley, New York. Cressie, N. and Hawkins, D. M. (1980), “Robust estimation of the variogram: I,” Journal of the Mathematical Association for Mathematical Geology, 12, 115-125.
18. Cressie, N. and Wikle, C. K. (2011), Statistics for Spatio-Temporal Data, Wiley, New York.
19. Creutin, J. D. and Obled, C. (1982), “Objective analysis and mapping techniques for rainfall fields: an objective comparison,” Water Resources Research, 18, 413-431.
20. Cui, H., Stein, A., and Myers, D. E. (1995), “Extension of spatial information, Bayesian kriging and updating of prior variogram parameters,” Environmetric, 6, 373-384.
21. Damian, D., Sampson, P. D., and Guttorp, P. (2000), “Bayesian estimation of semiparametric non-stationary spatial covariance structures,” Environmetrics, 12, 161-178.
22. David, M (1988), Handbook of Applied Advanced Geostatistical Ore Reserve Estimation, Elsevier Scientific Publishing.
23. de Boor, C. (1978), A Practical Guide to Splines, Springer, Berlin.
24. Delaunay, B. (1934), “Sur la sphere vide,” Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk, 7, 793-800.
25. Deville, J. C. (1974), “Méthodes statistiques et numériques de l’analyse harmonique,” Annales de l’INSEE, 15, 1-101.
26. Dirichlet, G. L. (1850), “Über die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen,” Journal fur die Reine und Angewandte Mathematik, 40, 209-227.
27. Donoho, D. L. and Johnstone, I. M. (1995), “Adapting to unknown smoothness via wavelet shrinkage,” Journal of the American Statistical Association, 90, 1200-1224.
28. Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., and Picard, D. (1995), “Wavelet shrinkage: Asymptopia?,” Journal of the Royal Statistics Society, Series B (Methodological), 57, 301-369.
29. Dowd, P. A. (1984), “The variogram and kriging: robust and resistant estimators,” Geostatistics for Natural Resources Characterization, Part I, edited by G. Verly, M. David, A. G. Journel, and A. Marechal, Reidel, Dordrecht, 91-106.
30. Durbáan, M., Currie, I.D., and Eilers, P.H.C. (2004), “Smoothing and forecasting mortality rates,” Statistical Modelling, 4, 279-298.
31. Eilers, P. H. and Marx, B. D. (1996), Flexible smoothing with B-splines and penalties (with discussion),” Statistical Science, 11, 89-121.
32. Eubank, R. (1999), Nonparametric Regression and Spline Smoothing, 2nd ed., Dekker, New York.
33. Fan, J. and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, Chapman and Hall, New York.
34. Friedman, J. H. (1991), “Multivariate adaptive regression splines,” Annals of Statistics, 19, 1-68.
35. Friedman, J. H. and Silverman, B. W. (1989), “Flexible parsimonious smoothing and additive modeling (with discussion),” Technometrics, 31, 3-39.
36. Fuentes, M. (2001), “A high frequency kriging approach for nonstationary environmental processes,” Environmetrics, 12, 469-483.
37. Fuentes, M. (2002), “Spectral methods for nonstationary spatial processes,” Biometrika, 89, 197-210.
38. Fuentes, M. and Smith, R. (2001), “A new class of nonstationary models,” Technical Report #2534, North Carolina State University, Institute of Statistics.
39. Goodchild, M. (1992), “Geographical information science,” International Journal of Geographic Information Systems, 6, 31-45.
40. Green, P. J. and Silverman, B. W. (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, New York.
41. Guttorp, P., Meiring, W., and Sampson, P. D. (1994), “A space-time analysis of ground-level ozone data,” Environmetrics, 5, 241-254.
42. Guttorp, P. and Sampson, P. D. (1994), “Methods for estimating heterogeneous spatial covariance functions with environmental applications,” Handbook of Statistics XII: Environmental Statistics, edited by G. P. Patil, and C. R. Rao, North Holland/Elsevier, New York, 663-690.
43. Guillot, G., Senoussi, R., and Monestiez, P. (2001), “Definite positive covariance estimator for nonstationary random fields,” GeoENV 2000: Third European Conference on Geostatistics for Environmental Applications, edited by P. Monestiez, D. Allard, and R. Froidevaux, Kluwer Academic Publishers, Dordrecht.
44. Hannachi, A., Jolliffe I. T., and Stephenson, D. B. (2007), “Empirical orthogonal functions and related techniques in atmospheric science: a review,” International Journal of Climatology, 27, 1119-1152.
45. Haas, T. C. (1990), “Lognormal and moving window methods of estimating acid deposition,” Journal of the American Statistical Association, 85, 950-963.
46. Haas, T. C. (1995), “Local prediction of a spatio-temporal process with an application to wet sulfate deposition,” Journal of the American Statistical Association, 90, 1189-1199.
47. Higdon, D. M. (1998), “A process-convolution approach to modeling temperatures in the North Atlantic Ocean,” Journal of Ecological and Environmental Statistics, 5, 173-190.
48. Higdon, D., Swall, J., and Kern, J. (1999), “Non-stationary spatial modeling,” Bayesian Statistics, 6th Edition, Oxford University Press, 761-768.
49. Holland, D., Saltzman, N., Cox, L., and Nychka, D. (1998), “Spatial prediction of sulfur dioxide in the eastern United States,” Geostatistics for Environmental Applications, edited by J. Gomez-Hernandez, A. Soares, and R. Froidevaux, Kluwer Academic Publishers, Dordrecht, 65-76.
50. Holmström, I. (1963), “On a method for parametric representation of the state of the atmosphere,” Tellua, 15, 127-149.
51. Hsu, N.-J., Chang, Y.-M., and Huang, H.-C. (2010), “Semiparametric estimation and selection for nonstationary spatial covariance functions,” Journal of Computational and Graphical Statistics, 19, 117-139.
52. Huang, C., Hsing, T., and Cressie, N. (2011), “Nonparametric estimation of varioram and its spectrum,” Biometrika, 98, 775-789.
53. Huang, J., Shen, H., and Buja, A. (2008), “Functional Principal Components Analysis via Penalized Rank One Approximation,” Electronic Journal of Statistics, 2, 678-695.
54. Jolliffe, I. T. (2002), Principal Component Analysis, second edition, Springer, New York.
55. Journel, A. G. and Huijbregts, Ch. J. (1978), Mining Geostatistics, Academic Press, London.
56. Karhunen, K. (1947), “Über lineare Methoden in der Wahrscheinlichkeitsrechnung,” Annales Academiae Scientiarum Fennicae, 37, 1-79.
57. Karl, T. R., Koscielny, A. J., and Diaz H. F. (1982), “Potential errors in the application of principal component (eigenvector) analysis to geophysical data,” Journal of Applied Meteorology, 21, 1183-1186.
58. Lele, S. (1997), “Estimating functions for semivariogram estimation,” Selected Proceedings of the Conference on Estimating Functions. Institute of Mathematical Statistics, edited by I.V. Basawa, V.P. Godambe, and R.L. Taylor, Hayward, California, 381-396.
59. Liang K.-Y. and Zeger, S. L. (1986), “Longitudinal data analysis using generalized linear models,” Biometrika, 73, 13-22.
60. Loève, M. (1978), Probability Theory, Springer-Verlag, New York.
61. Lorenz, E. N. (1956), “Empirical orthogonal functions and statistical weather prediction,” Scientific Report No. 1, Statistical Forecasting Project, Department of Meteorology, Massachusetts Institute of Technology.
62. Mardia, K. V. and Goodall, C. R. (1992), “Spatial-temporal analysis of multivariate environmental monitoring data,” Multivariate Environmental Statistics 6, edited by N. K. Bose, G. P. Patil, and C. R. Rao, North Holland, New York, 347-385.
63. Matérn, B. (1986), Spatial Variation, Lecture Notes in Statistics, Springer, New York.
64. Matheron, G. (1962), “Traité de géostatistique appliquée, Tome I,” Memoires du Bureau de Recherches Geologiques et Minieres, 14, Editions Technip, Paris.
65. Matheron, G. (1963), “Principles of geostatistics,” Economic Geology, 58, 1246-1266.
66. Meiring, W. (1995), “Estimation of Heterogeneous Space-Time Covariance,” PhD thesis, University of Washington, Seattle.
67. Meiring, W., Guttorp, P., and Sampson, P. D. (1998), “Computational issues in fitting spatial deformation models for heterogeneous spatial correlation,” Computing Science and Statistics, edited by D. W. Scott, 29, 409-417.
68. Meiring, W., Monestiez, P., Sampson, P. D. , (1997), “Developments in the modelling of nonstationary spatial covariance structure from space-time monitoring data,” Geostatistics Wollongong ’96, 1, edited by E. Y. Baafi and N. Schofield, Kluwer Academic Publishers, 162-173.
69. Meng, X. and Rubin, D. B. (1993), “Maximum likelihood estimation via the ECM algorithm: a general framework”, Biometrika, 80, 267-278.
70. Noirie, D. H. and DeVries, G. (1973), The finite element method, Academic Press.
71. Nott, D. J. and Dunsmuir, T. M. (2002), “Estimation of nonstationary spatial covariance structure,” Biometrika, 89, 819-829.
72. Nychka, D. and Saltzman, N. (1998), “Design of air quality networks,” Case Studies in Environmental Statistics, edited by D. Nychka, W. Piegorsch, and L. Cox, Springer-Verlag, New York, 51-76.
73. Nychka, D., Wikle, C., and Royle, J. A. (2000), “Large spatial prediction problems and nonstationary random fields,” Technical report, National Center for Atmospheric Research.
74. Obled, C. and Creutin, J. D. (1986), “Some developments in the use of empirical orthogonal functions for mapping meteorological fields,” Journal of Climate and Applied meteorology, 25, 1189-1204.
75. Obukhov, A. M. (1960), “The statistically orthogonal expansion of empirical functions,” Bulletin of the Academy of Sciences of the U.S.S.R.: Geophysics Series, 1, 288-291.
76. Omre, H. (1984), “The variogram and its estimation,” Geostatistics for Natural Resources Characterization, Part I, edited by G. Verly, M. David, A. Journel, and A. Marechal, Reidel, Dordrecht, 107-125.
77. Omre, H. (1987), “Bayesian Kriging - merging observations and qualified guesses in kriging,” Mathematical Geology, 19, 25-39.
78. Omre, H. and Halvorsen, K. B. (1989), “The Bayesian bridge between simple and universal Kriging,” Mathematical Geology, 21, 767-786.
79. Paciorek, C. J. and Schervish, M. J. (2006), “Spatial modelling using a new class of nonstationary covariance functions,” Environmetrics, 17, 483-506.
80. Perrin, O. and Senoussi, R. (2000), “Reducing non-stationary random fields to stationarity and isotropy using a space deformation,” Statistics and Probability Letters, 48, 23-32.
81. Preisendorfer R. W. (1988), Principal Component Analysis in Meteorology and Oceanography, Elsevier, Amsterdam.
82. Rao, C. R. (1971), “Minimum variance quadratic unbiased estimation of variance components,” Journal of Multivariate Analysis, 1, 445-456.
83. Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge University Press, Cambridge.
84. Sampson, P. D., Damian, D., and Guttorp, P. (2001), “Advances in modeling and inference for environmental processes with nonstationary spatial covariance,” Geostatistics for Environmental Applications, edited by J. Gomez-Hernandez, A. Soares, and R. Froidevaux, Kluwer Academic Publishers, Dordrecht, 17-32.
85. Sampson, P. D. and Guttorp, P. (1992), “Nonparametric estimation of nonstationary spatial covariance structure,” Journal of the American Statistical Association, 87, 108-119.
86. Schabenberger, O. and Gotway, C. A. (2005), Statistical Methods for Spatial Data Analysis, Chapman and Hall, New York.
87. Schmidt, A. M. and O’Hagan, A. (2003), “Bayesian inference for nonstationary spatial covariance structure via spatial deformations,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65, 743-758.
88. Schoenberg, I. J. (1946), “Contribution to the problem of approximation of equidistant data by analytic functions,” Quarterly of Applied Mathematics, 4, 45-99 & 112-141.
89. Shimamura, T., Imoto, S., Yamaguchi, R., and Miyano, S. (2007), “Weighted lasso in graphical Gaussian modeling for large gene network estimation based on microarray data,” Genome Informatics, 19, 142-153.
90. Smith, R. L. (1996), “Estimating nonstationary spatial correlations,” Preliminary version: on the Spatial Statistics Preprint Service at http://hp2.niss.rti.org/organization/personnel/granville/list.html
91. Smith, M. and Kohn, R. (1996), “Nonparametric regression via Bayesian variable selection,” Journal of Econometrics, 75, 17-344.
92. Stein, A. (1994), “The use of prior information in spatial statistics,” Geoderma, 62, 199-216.
93. Stone, C.J., Hansen, M., Kooperberg, C., and Truong, Y. K. (1997), “Polynomial splines and their tensor products in extended linear modeling (with discussion),” Annals of Statistics, 25, 1371-1470
94. Tateishi, S., Matsui, H., and Konishi, S. (2010), “Nonlinear regression modeling via the lassotype regularization,” Journal of Statistical Planning and Inference, 140, 1125-1134.
95. Tibshirani, R. (1996), “Regression shrinkage and selection via the LASSO,” Journal of the Royal Statistical Scoiety, Series B, 58, 267-288.
96. Voronoi, G. (1907), “Nouvelles applications des paramètres continus à la théorie des formes quadratiques,” Journal fur die Reine und Angewandte Mathematik, 133, 97-178.
97. Wahba, G. (1990), Spline Models for Observational Data, Society for Industrial and Applied Mathematics, Philadelphia.
98. Wand, M.P. and Jones, M.C. (1995), Kernel Smoothing,Chapman and Hall, New York.
99. Wikle, C. K. and Cressie, N. (1999), “A dimension-reduced approach to space-time Kalman filtering,” Biometrika, 86, 815-829.
100. Wilks, D. S. (1995), Statistical Methods in the Atmospheric Sciences, Academic Press, San Diego.
101. Yaglom, A. M. ( 1987), Correlation Theory of Stationary and Related Randorm Functions, Vol. I: Basic Results; Vol. II: Supplementary Notes and References. Springer, New York.
102. Yao, F. and Lee, T. C., (2006), “Penalized spline models for functional principal component analysis,” Journal of the Royal Statistical Society, Series B, 68, 3-25.
103. Yao, F., Müller, H. G., and Wang, J. L. (2005), “Functional data analysis for sparse longitudinal data,” Journal of the American Statistical Association, 100, 577-590.
104. Zeger, S. L. and Liang, K.-Y. (1986), “Longitudinal data analysis for discrete and continuous outcomes,” Biometrics, 42, 121-130.
105. Zhou, L., Huang, J. Z., and Carroll, R. J. (2008), “Joint modeling of paired sparse functional data using principal components,” Biometrika, 95, 601-619.
106. Zou, H. (2006), “The adaptive Lasso and its oracle properties,” Journal of the American Statistical Association, 101, 1418-1429.

指導教授

黃信誠、傅承德
(Hsin-Cheng Huang、Cheng-Der Fuh)

審核日期

2013-1-17

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