Robust, adaptive functional regression in functional mixed model framework

Journal of the American Statistical Association

Volumn 106, Issue 495, 2011, Pages 1167-1179

  Zhu, Hongxiao ^a   Brown, Philip J ^b   Morris, Jeffrey S ^c  

^a Statistical and Applied Mathematical Sciences Institute USA   (United States)

^b UNIVERSITY OF KENT   (United Kingdom)

^c UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

Author keywords

Adaptive LASSO; Bayesian methods; False discovery rate; Functional Data Analysis; Robust regression; Scale mixtures of normals; Sparsity Priors; Variable Selection; Wavelets

Indexed keywords

EID: 80054702555     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2011.tm10370     Document Type: Article

References (51)

1. Andrews, D. F., and Mallows, C. L. (1974), "Scale Mixtures of Normal Distributions, " Journal of the Royal Statistical Society, Ser. B, 36, 99-102. [1172]
2. Aston, J., Chiou, J.-M., and Evans, J. (2010), "Linguistic Pitch Analysis Using Functional Principal Component Mixed Effect Models, " Journal of the Royal Statistical Society, Ser. C, 59, 297-317. [1173]
3. Ayers, K. L., and Cordell, H. J. (2006), "SNP Selection in Genome-Wide and Candidate Gene Studies via Penalized Logistic Regression, " Genetic Epidemiology, 34, 879-891. [1170]
4. Baladandayuthapani, V., Mallick, B. K., Hong, M. Y., Lupton, J. R., Turner, N. D., and Carroll, R. J. (2008), "Bayesian Hierarchical Spatially Correlated Functional Data AnalysisWith Application to Colon Carcinogenesis, " Biometrics, 64, 64-73. [1167]
5. Brumback, B. A., and Rice, J. A. (1998), "Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves, " Journal of the American Statistical Association, 93, 961-976. [1167]
6. Carvalho, C. M., Polson, N. G., and Scott, J. G. (2010), "The Horseshoe Estimator for Sparse Signals, " Biometrika, 97 (2), 465-480. [1170]
7. Clyde, M., and George, E. I. (2000), "Flexible Empirical Bayes Estimation for Wavelets, " Journal of the Royal Statistical Society, Ser. B, 62, 681-698. [1170]
8. Crambes, C., Delsol, L., and Laksaci, A. (2008), "Robust Nonparametric Estimation for Functional Data, " Journal of Nonparametric Statistics, 20 (7), 573-598. [1168]
9. Cutillo, L., Jung, Y. Y., Ruggeri, F., and Vidakovic, B. (2008), "Larger Posterior Mode Wavelet Thresholding and Applications, " Journal of Statistical Planning and Inference, 138, 3758-3773. [1170]
10. Dawid, A. P. (1981), "Some Matrix-Variate Distribution Theory: Notational Considerations and a Bayesian Application, " Biometrika, 68, 265-274. [1168]
11. Di, C., Crainiceanu, C. M., Caffo, B. S., and Punjabi, N. M. (2009), "Multilevel Functional Principal Component Analysis, " The Annals of Applied Statistics, 3 (1), 458-488. [1167]
12. Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis, New York: Springer-Verlag. [1167]
13. Gervini, D. (2008), "Robust Functional Estimation Using the Median and Spherical Principal Components, " Biometrika, 95 (3), 587-600. [1168]
14. Gervini, D. (2010), "Detecting and Handling Outlying Trajectories in Irregularly Sampled Functional Datasets, " The Annals of Applied Statistics, 3, 1758-1775. [1168]
15. Greven, S., Crianiceanu, C. M., Caffo, B. S., and Reich, D. (2010), "Longitudinal Functional Principal Component Analysis, " Electronic Journal of Statistics, 4, 1022-1059. [1167]
16. Griffin, J. E., and Brown, P. J. (2005), "Alternative Prior Distributions for Variable Selection With Very Many More Variables Than Observations, " CRiSM Working Paper 05-10, University of Warwick. [1170,1177]
17. Griffin, J. E., and Brown, P. J. (2010), "Inference With Normal-Gamma prior Distributions in Regression Problems, " Bayesian Analysis, 5 (1), 171-188. [1171]
18. Guo, W. (2002), "Functional Mixed Effects Models, " Biometrics, 58, 121-128. [1167]
19. Hampel, F. R., Ronchetti, E. M., Rousseauw, P. J., and Stahel, W. A. (2005), Robust Statistics: The Approach Based on Influence Functions (2nd ed.), New York: Wiley. [1167]
20. Herrick, R. C., and Morris, J. S. (2006), "Wavelet-Based Functional Mixed Model Analysis: Computational Considerations, " in Proceedings, Joint Statistical Meetings, ASA Section on Statistical Computing, Alexandria, VA: American Statistical Association, pp. 2051-2053. [1178]
21. Huber, P. (1981), Robust Statistics, New York: Wiley. [1167]
22. Hubert, M., Rousseeuw, P. J., and Verboven, S. (2002), "A Fast Method for Robust Principal Components With Applications to Chemometrics, " Chemometrics and Intelligent Laboratory Systems, 60, 101-111. [1168]
23. Johnstone, I. M., and Silverman, B. W. (2004), "Needles and Straw in Haystacks: Empirical Bayes Estimates of Possibly Sparse Sequences, " The Annals of Statistics, 32, 1594-1649. [1170,1171]
24. Johnstone, I. M., and Silverman, B. W. (2005), "Empirical Bayes Selection of Wavelet Thresholds, " The Annals of Statistics, 33, 1700-1752. [1171]
25. Jung, S., and Marron, J. S. (2009), "PCA Consistency in High Dimension, Low Sample Size Context, " The Annals of Statistics, 37 (6B), 4104-4130. [1178]
26. Kokoszka, P., Maslova, I., Sojka, J., and Zhu, L. (2006), "Probability Tails of Wavelet Coefficients of Magnetometer Records, " Journal of Geophysical Research, 111, 1-15. [1170]
27. Locantore, N., Marron, J. S., Simpson, D. G., Tripoli, N., Zhang, J. T., and Cohen, K. L. (1999), "Robust Principal Component Analysis for Functional Data, " Test, 8 (1), 1-73. [1168]
28. Morris, J. S., and Carroll, R. J. (2006), "Wavelet-Based Functional Mixed Models, " Journal of the Royal Statistical Society, Ser. B, 68, 179-199. [1167-1169,1171,1172,1176]
29. Morris, J. S., Arroyo, C., Coull, B. A., Louise, M. R., Herrick, R., and Gortmaker, S. (2006), "Using Wavelet-Based Functional Mixed Models to Characterize Population Heterogeneity in Accelerometer Profiles: A Case Study, " Journal of the American Statistical Association, 101, 1352-1364. [1167]
30. Morris, J. S., Baladandayuthapani, V., Herrick, R. C., Sanna, P., and Gutstein, H. (2011), "Automated Analysis of Quantitative Image Data Using Isomorphic Functional Mixed Models, With Application to Proteomics Data, " The Annals of Applied Statistics, 5 (2A), 894-923. [1167,1169,1171,1172,1178]
31. Morris, J. S., Brown, P. J., Herrick, R. C., Baggerly, K. A., and Coombes, K. R. (2008), "Bayesian Analysis of Mass Spectrometry Proteomics Data Using Wavelet Based FunctionalMixed Models, " Biometrics, 64, 479-489. [1171, 1175,1176]
32. Morris, J. S., Coombes, K. R., Kooman, J., Baggerly, K. A., and Kobayashi, R. (2005), "Feature Extraction and Quantification for Mass Spectrometry Data in Biomedical Applications Using the Mean Spectrum, " Bioinformatics, 21 (9), 1764-1775. [1175]
33. Morris, J. S., Vannucci, M., Brown, P. J., and Carroll, R. J. (2003), "Wavelet-Based Nonparametric Modeling of Hierarchical Functions in Colon Carcinogenesis, " Journal of the American Statistical Association, 98, 573-583. [1167]
34. Nason, G. P. (ed.) (2008), Wavelet Methods in Statistics With R, New York: Springer. [1171]
35. Ogden, R. (1997), Essential Wavelets for Statistical Applications and Data Analysis, Boston: Birkhäuser. [1168]
36. Park, T., and Casella, G. (2008), "The Bayesian Lasso, " Journal of the American Statistical Association, 103, 681-686. [1170]
37. Pensky, M. (2006), "Frequentist Optimality of Bayesian Wavelet Shrinkage Rules for Gaussian and Non-Gaussian Noise, " The Annals of Statistics, 34 (2), 769-807. [1170]
38. Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis, (2nd ed.), New York: Springer. [1167]
39. Ruppert, D., Wand, M. P., and Carroll, R. J. (2009), "Semiparametric Regression During 2003-2007, " Electronic Journal of Statistics, 3, 1193-1256. [1167]
40. Searle, S. R., Casella, G., and McCulloch, C. E. (eds.) (1992), Variance Components, New York: Wiley. [1171,1174]
41. Staicu, A. M., Crainiceanu, C. M., and Carroll, R. J. (2010), "Fast Methods for Spatially Correlated Multilevel Functional Data, " Biostatistics, 11 (2), 177-194. [1167]
42. Staniswallis, J. G., and Lee, J. J. (1998), "Nonparametric Regression Analysis of Longitudinal Data, " Journal of the American Statistical Association, 93, 1403-1418. [1167]
43. Tibshirani, R. (1996), "Regression Shrinkage and Selection via the Lasso, " Journal of the Royal Statistical Society, Ser. B, 58, 267-288. [1170]
44. Vidakovic, B. (1999), Statistical Modeling by Wavelets, New York: Wiley. [1168-1170]
45. Vidakovic, B., and Ruggeri, F. (2001), "BAMs Method: Theory and Simulations, " The Indian Journal of Statistics, 63, 234-249. [1170,1171]
46. Wang, Y. (1998), "Mixed Effects Smoothing Spline Analysis of Variance, " Journal of the Royal Statistical Society, Ser. B, 60, 159-174. [1167]
47. West, M. (1987), "On Scale Mixtures of Normal Distributions, " Biometrika, 74, 646-648. [1172]
48. Wu, H., and Zhang, J. T. (2002), "Local Polynomial Mixed-Effect Models for Longitudinal Data, " Journal of the American Statistical Association, 97, 883-897. [1167]
49. Zhou, L., Huang, J. Z., Martinez, J. G., Maity, A., Baladandayuthapani, V., and Carroll, R. J. (2010), "Reduced Rank Mixed Effects Models for Spatially Correlated Hierarchical Functional Data, " Journal of the American Statistical Association, 105, 390-400. [1167]
50. Zipunnikov, V., Caffo, B. S., Crainiceanu, C. M., Yousem, D. M., Davatzikos, C., and Schwartz, B. S. (2010), "Multilevel Functional Principal Component Analysis for High-Dimensional Data, " Working Paper 219, Johns Hopkins University, Dept. of Biostatistics, available at http://www.bepress.com/ jhubiostat/paper219. [1167]
51. Zou, H. (2006), "The Adaptive Lasso and Its Oracle Properties, " Journal of the American Statistical Association, 101, 1418-1429. [1170]