Covariate Dependent Sparse Functional Data Analysis

References

• Bachrach LK, Hastie T, Wang MC, Narasimhan B, Marcus R (1999) Bone mineral acquisition in healthy Asian, Hispanic, Black, and Caucasian youth: A longitudinal study. J. Clinical Endocrinology Metabolism 84(12):4702–4712.Google Scholar
• Cardot H (2007) Conditional functional principal components analysis. Scandinavian J. Statist. 34(2):317–335.Google Scholar
• Chehade A, Liu K (2019) Structural degradation modeling framework for sparse datasets with an application on Alzheimer’s disease. IEEE Trans. Automation Sci. Engrg. 16(1):192–205.Google Scholar
• Chiou JM, Chen YT, Yang YF (2014) Multivariate functional principal component analysis: A normalization approach. Statist. Sinica 24(4):1571–1596.Google Scholar
• Chung S, Kontar R (2020) Functional principal component analysis for extrapolating multi-stream longitudinal data. IEEE Trans. Reliability 70(4):1321–1331.Google Scholar
• Dekkers AL, Einmahl JH, De Haan L (1989) A moment estimator for the index of an extreme-value distribution. Ann. Statist. 17(4):1833–1855.Google Scholar
• Ding F, He S, Jones DE, Huang JZ (2020) Supervised functional PCA with covariate dependent mean and covariance structure. Preprint, submitted January 30, https://arxiv.org/abs/2001.11425.Google Scholar
• Ding F, He S, Jones DE, Huang JZ (2022) Functional PCA with covariate-dependent mean and covariance structure. Technometrics 64(3):335–345.Google Scholar
• Fan J, Gijbels I (1996) Local Polynomial Modelling and Its Applications (Routledge).Google Scholar
• Fang X, Yan H, Gebraeel N, Paynabar K (2021) Multi-sensor prognostics modeling for applications with highly incomplete signals. IISE Trans. 53(5):597–613.Google Scholar
• Garner FA (2020) Radiation-induced damage in austenitic structural steels used in nuclear reactors. Comprehensive Nuclear Materials, vol. 3, 2nd ed. (Elsevier, New York), 57–168.Google Scholar
• Guo W (2002) Functional mixed effects models. Biometrics 58:121–128.Google Scholar
• Hoffman MD, Gelman A (2014) The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. J. Machine Learn. Res. 15(1):1593–1623.Google Scholar
• Jiang CR, Wang JL (2010) Covariate adjusted functional principal components analysis for longitudinal data. Annals Statist. 38(2):1194–1226.Google Scholar
• Jin M, Cao P, Short MP (2019) Predicting the onset of void swelling in irradiated metals with machine learning. J. Nuclear Materials 523:189–197.Google Scholar
• Kim M, Liu K (2020) A Bayesian deep learning framework for interval estimation of remaining useful life in complex systems by incorporating general degradation characteristics. IISE Trans. 53(3):326–340.Google Scholar
• Kim M, Song C, Liu K (2021) Individualized degradation modeling and prognostics in a heterogeneous group via incorporating intrinsic covariate information. IEEE Trans. Automation Sci. Engrg. 19(3):2079–2094.Google Scholar
• Li G, Shen H, Huang JZ (2016) Supervised sparse and functional principal component analysis. J. Comput. Graphical Statist. 25(3):859–878.Google Scholar
• Li J, Huang C, Hongtu Z (2017) A functional varying-coefficient single-index model for functional response data. J. Amer. Statist. Assoc. 112(519):1169–1181.Google Scholar
• Lin Y, Liu K, Byon E, Qian X, Liu S, Huang S (2018) A collaborative learning framework for estimating many individualized regression models in a heterogeneous population. IEEE Trans. Reliability 67(1):328–341.Google Scholar
• Linkletter C, Bingham D, Hengartner N, Higdon D, Ye KQ (2006) Variable selection for Gaussian process models in computer experiments. Technometrics 48(4):478–490.Google Scholar
• Looker AC, Melton LJ, Harris T, Borrud L, Shepherd J, McGowan J (2009) Age, gender, and race/ethnic differences in total body and subregional bone density. Osteoporosis Internat. 20(7):1141–1149.Google Scholar
• Mccormick DP, Ponder SW, Fawcett HD, Palmer JL (1991) Spinal bone mineral density in 335 normal and obese children and adolescents: Evidence for ethnic and sex differences. J. Bone Mineral Res. 6(5):507–513.Google Scholar
• Mercer J (1909) Functions of positive and negative type, and their connection with the theory of integral equations. Proc. Royal Soc. London Ser. A 83(559):69–70.Google Scholar
• Moon H, Dean AM, Santner TJ (2012) Two-stage sensitivity-based group screening in computer experiments. Technometrics 54(4):376–387.Google Scholar
• Neal RM (1995) Bayesian learning for neural networks. PhD thesis, University of Toronto, Toronto.Google Scholar
• Neal RM (1997) Monte Carlo implementation of Gaussian process models for Bayesian regression and classification. Technical Report Issue 9702, Department of Statistics, University of Toronto, Toronto.Google Scholar
• Patel DN, Pettifor JM, Becker PJ, Grieve C, Leschner K (1992) The effect of ethnic group on appendicular bone mass in children. J. Bone Mineral Res. 7(3):263–272.Google Scholar
• Peng W, Li YF, Mi J, Yu L, Huang HZ (2016) Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective. Reliability Engrg. Systems Safety 153:75–87.Google Scholar
• Piironen J, Vehtari A (2016) Projection predictive model selection for gaussian processes. Palmieri FAN, ed. Proc. IEEE 26th Internat. Workshop on Machine Learn. for Signal Processing (IEEE, New York), 1–6 (IEEE, New York).Google Scholar
• Ramsay JO, Dalzell C (1991) Some tools for functional data analysis. J. Royal Statist. Soc. B 53(3):539–561.Google Scholar
• Rasmussen CE (1996) Evaluation of Gaussian processes and other methods for non-linear regression. PhD thesis, Department of Computer Science, University of Toronto, Toronto.Google Scholar
• Rice JA, Silverman BW (1991) Estimating the mean and covariance structure nonparametrically when the data are curves. J. Royal Statist. Soc. Ser. B 53(1):233–243.Google Scholar
• Silverman BW (1998) Density Estimation for Statistics and Data Analysis. Density Estimation: For Statistics and Data Analysis 1–175, 1st ed. (Chapman & Hall, New York).Google Scholar
• Wang H, Xia Y (2017) Shrinkage estimation of the varying coefficient model. J. Amer. Statist. Assoc. 13(2):76–87.Google Scholar
• Wang JL, Chiou JM, Müller HG, Mueller HG (2016) Review of functional data analysis. Annual Rev. Statist. Appl. 3(1):257–295.Google Scholar
• Was GS (2007) Fundamentals of Radiation Materials Science: Metals and Alloys, 1st ed. (Springer Berlin, Heidelberg).Google Scholar
• Wu Y, Boos DD, Stefanski LA (2007) Controlling variable selection by the addition of pseudovariables. J. Amer. Statist. Assoc. 102(477):235–243.Google Scholar
• Xu Z, Hong Y, Jin R (2016) Nonlinear general path models for degradation data with dynamic covariates. Appl. Stochastic Models Bus. Industry 32(2):153–167.Google Scholar
• Yan H, Liu K, Zhang X, Shi J (2016) Multiple sensor data fusion for degradation modeling and prognostics under multiple operational conditions. IEEE Trans. Reliability 65(3):1416–1426.Google Scholar
• Yao F, Müller HG, Wang JL (2005) Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100(470):577–590.Google Scholar
• Zhang H (2004) Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics. J. Amer. Statist. Assoc. 99(465):250–261.Google Scholar