Park, So Young; Xiao, Luo; Willbur, Jayson D.; Staicu, Ana-Maria; Jumbe, N. L’ntshotsholé A joint design for functional data with application to scheduling ultrasound scans. (English) Zbl 1469.62127 Comput. Stat. Data Anal. 122, 101-114 (2018). Summary: A joint design for sampling functional data is proposed to achieve optimal prediction of both functional data and a scalar outcome. The motivating application is fetal growth, where the objective is to determine the optimal times to collect ultrasound measurements in order to recover fetal growth trajectories and to predict child birth outcomes. The joint design is formulated using an optimization criterion and implemented in a pilot study. Performance of the proposed design is evaluated via simulation study and application to fetal ultrasound data. Cited in 2 Documents MSC: 62-08 Computational methods for problems pertaining to statistics 62R10 Functional data analysis 62P10 Applications of statistics to biology and medical sciences; meta analysis Keywords:covariance function; functional data analysis; fetal growth; longitudinal data; prediction Software:fda (R); R; shiny PDF BibTeX XML Cite \textit{S. Y. Park} et al., Comput. Stat. Data Anal. 122, 101--114 (2018; Zbl 1469.62127) Full Text: DOI OpenURL References: [1] Atkinson, A. C.; Donev, A. N.; Tobias, R. D., Optimum experimental designs, with SAS, (2007), Oxford New York · Zbl 1183.62129 [2] Bohorquez, M.; Giraldo, R.; Mateu, J., Optimal sampling for spatial prediction of functional data, Stat. Methods Appl., 25, 39-54, (2015) · Zbl 1416.62542 [3] Bunea, F.; Xiao, L., On the sample covariance matrix estimator of reduced effective rank population matrices, with applications to fpca, Bernoulli, 21, 2, 1200-1230, (2015) · Zbl 1388.62173 [4] Chang, W., Cheng, J., Allaire, J., Xie, Y., McPherson, J., 2016. shiny: Web Application Framework for R. R package version 0.13.2. [5] Crainiceanu, C.; Staicu, A.; Ray, S.; Punjabi, N., Bootstrap-based inference on the difference in the means of two correlated functional processes, Stat. Med., 31, 3223-3240, (2012) [6] Delaigle, A.; Hall, P.; Bathia, N., Componentwise classification and clustering of functional data, Biometrika, 99, 299-313, (2012) · Zbl 1244.62090 [7] Ferraty, F.; Hall, P.; Vieu, P., Most-predictive design points for functional data predictors, Biometrika, 97, 4, 807-824, (2010) · Zbl 1204.62064 [8] Goldsmith, J.; Kitago, T., Assessing systematic effects of stroke on motor control by using hierarchical function-on-scalar regression, J. R. Stat. Soc. Ser. C. Appl. Stat., 65, 2, 215-236, (2016) [9] Greven, S.; Crainiceanu, C.; Caffo, B.; Reich, D., Longitudinal functional principal component analysis, Electron. J. Stat., 4, 1022-1054, (2010) · Zbl 1329.62334 [10] Horváth, L.; Kokoszka, P., Inference for functional data with applications, (2012), Springer New York · Zbl 1279.62017 [11] James, G.; Hastie, T.; Sugar, C., Principal component models for sparse functional data, Biometrika, 87, 587-602, (2000) · Zbl 0962.62056 [12] Ji, H.; Müller, H.-G., Optimal designs for longitudinal and functional data, J. R. Stat. Soc. Ser. B Stat. Methodol., 79, 3, 859-876, (2017) [13] Jiang, C.-R.; Aston, J. A.; Wang, J.-L., Smoothing dynamic positron emission tomography time courses using functional principal components, NeuroImage, 47, 1, 184-193, (2009) [14] Li, H.; Staudenmayer, J.; Carroll, R. J., Hierarchical functional data with mixed continuous and binary measurements, Biometrics, 70, 4, 802-811, (2014) · Zbl 1393.62076 [15] Lindquist, M. A., Functional causal mediation analysis with an application to brain connectivity, J. Amer. Statist. Assoc., 107, 500, 1297-1309, (2012) · Zbl 1258.62105 [16] Lu, X.; Marron, J. S., Analysis of spike train data: comparison between the real and the simulated data, Electron. J. Stat., 8, 2, 1793-1796, (2014) · Zbl 1305.62330 [17] Morris, J.; Arroyo, C.; Coull, B.; Ryan, L.; Herrick, R.; Gortmaker, S., Using wavelet-based functional mixed models to characterize population heterogeneity in accelerometer profiles: a case study, J. Amer. Statist. Assoc., 101, 1352-1364, (2006) · Zbl 1171.62357 [18] Park, S. Y.; Staicu, A.-M., Longitudinal functional data analysis, Stat, 4, 1, 212-226, (2015) [19] Peng, J.; Paul, D., A geometric approach to maximum likelihood estimation of functional principal components from sparse longitudinal data, J. Comput. Graph. Statist., 18, 995-1015, (2009) [20] R: A language and environment for statistical computing, (2016), R Foundation for Statistical Computing Vienna, Austria [21] Ramsay, J.; Silverman, B., Functional data analysis, (2005), Springer New York · Zbl 1079.62006 [22] Ramsay, J.; Silverman, B. W., Applied functional data analysis: methods and case studies, (2002), Springer New York · Zbl 1011.62002 [23] Randolph, T. W.; Harezlak, J.; Feng, Z., Structured penalties for functional linear models - partially empirical eigenvectors for regression, Electron. J. Stat., 6, 323-353, (2012) · Zbl 1274.62455 [24] Rasekhi, M.; Jamshidi, B.; Rivaz, F., Optimal location design for prediction of spatial correlated environmental functional data, J. Mod. Appl. Statist. Meth., 13, 2, 26, (2014) [25] Reimherr, M.; Nicolae, D., A functional data analysis approach for genetic association studies, Ann. Appl. Stat., 8, 1, 406-429, (2014) · Zbl 1454.62385 [26] Reiss, P. T.; Ogden, R. T., Functional generalized linear models with images as predictors, Biometrics, 66, 1, 61-69, (2010) · Zbl 1187.62112 [27] Ritter, K., Asymptotic optimality of regular sequence designs, Ann. Statist., 24, 5, 2081-2096, (1996) · Zbl 0905.62077 [28] Tang, R.; Müller, H., Time-synchronized clustering of gene expression trajectories, Biostatistics, 10, 32-45, (2009) [29] Wu, M.; Diez-Roux, A.; Raghunathan, T. E.; Sanchez, B. N., FPCA-based method to select optimal sampling schedules that capture between-subject variability in longitudinal studies, Biometrics, n/a-n/a, (2017) [30] Xiao, L.; Huang, L.; Schrack, J. A.; Ferrucci, L.; Zipunnikov, V.; Crainiceanu, C. M., Quantifying the lifetime Circadian rhythm of physical activity: a covariate-dependent functional approach, Biostatistics, 16, 2, 352-367, (2015) [31] Xiao, L.; Li, C.; Checkley, W.; Crainiceanu, C., Fast covariance estimation for sparse functional data, Stat. Comput, (2017) [32] Yao, F.; Müller, H.; Wang, J., Functional data analysis for sparse longitudinal data, J. Amer. Statist. Assoc., 100, 577-590, (2005) · Zbl 1117.62451 [33] Ylvisaker, D., Prediction and design, Ann. Statist., 15, 1, 1-19, (1987) · Zbl 0646.62080 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.