References
- Bhattacharya, P. K., and Gangopadhyay, A. K. (1990), “Kernel and Nearest-neighbor Estimation of a Conditional Quantile,” The Annals of Statistics, 18, 1400–1415. DOI: 10.1214/aos/1176347757.
- Bigot, J., Gouet, R., Klein, T., and López, A. (2017), “Geodesic PCA in the Wasserstein space by convex PCA,” Annales de l’Institut Henri Poincaré B: Probability and Statistics, 53, 1–26. DOI: 10.1214/15-AIHP706.
- Delicado, P. (2007), “Functional k-sample Problem When Data Are Density Functions,” Computational Statistics, 22, 391–410. DOI: 10.1007/s00180-007-0047-y.
- Delicado, P. (2011), “Dimensionality Reduction When Data Are Density Functions,” Computational Statistics, 55, 401–420.
- Dunson, D., Pillai, N., and Park, J.-H. (2007), “Bayesian Density Regression,” Journal of the Royal Statistical Society, Series B, 69, 163–183. DOI: 10.1111/j.1467-9868.2007.00582.x.
- Egozcue, J. J., Diaz-Barrero, J. L., and Pawlowsky-Glahn, V. (2006), “Hilbert Space of Probability Density Functions Based on Aitchison Geometry,” Acta Mathematica Sinica, 22, 1175–1182. DOI: 10.1007/s10114-005-0678-2.
- Gajek, L. (1986), “On Improving Density Estimators Which Are Not Bona Fide Functions,” Annals of Statistics, 14, 1612–1618. DOI: 10.1214/aos/1176350182.
- Hall, P., and Müller, H.-G. (2003), “Order-preserving Nonparametric Regression, With Applications to Conditional Distribution and Quantile Function Estimation,” Journal of the American Statistical Association, 98, 598–608. DOI: 10.1198/016214503000000512.
- Hall, P., Wolff, R. C. L., and Yao, Q. (1999), “Methods for Estimating a Conditional Distribution Function,” Journal of the American Statistical Association, 94, 154–163. DOI: 10.1080/01621459.1999.10473832.
- Han, K., Müller, H.-G., and Park, B. U. (2018), “Smooth Backfitting for Additive Modeling With Small Errors-in-variables, With an Application to Additive Functional Regression for Multiple Predictor Functions,” Bernoulli, 24, 1233–1265. DOI: 10.3150/16-BEJ898.
- Kneip, A. and Utikal, K. J. (2001), “Inference for Density Families Using Functional Principal Component Analysis,” Journal of the American Statistical Association, 96, 519–542. DOI: 10.1198/016214501753168235.
- Koenker, R., Ng, P., and Portnoy, S. (1994), “Quantile Smoothing Splines,” Biometrika, 81, 673–680. DOI: 10.1093/biomet/81.4.673.
- Lee, Y. K., Mammen, E., and Park, B. U. (2010), “Backfitting and Smooth Backfitting for Additive Quantile Models,” Annals of Statistics, 38, 2857–2883. DOI: 10.1214/10-AOS808.
- Lee, Y. K., Mammen, E., and Park, B. U. (2012), “Flexible Generalized Varying Coefficient Regression Models,” Annals of Statistics, 40, 1906–1933.
- Li, Q., Lin, J., and Racine, J. S. (2013), “Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions,” Journal of Business & Economic Statistics, 31, 57–65. DOI: 10.1080/07350015.2012.738955.
- Mammen, E., Linton, O., and Nielsen, J. (1999), “The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions,” Annals of Statistics, 27, 1443–1490. DOI: 10.1214/aos/1017939138.
- Mammen, E., and Park, B. U. (2006), “A Simple Smooth Backfitting Method for Additive Models,” Annals of Statistics, 34, 2252–2271. DOI: 10.1214/009053606000000696.
- Menafoglio, A., Guadagnini, A., and Secchi, P. (2014), “A Kriging Approach Based on Aitchison Geometry for the Characterization of Particle-size Curves in Heterogeneous Aquifers,” Stochastic Environmental Rearch and Risk Assessment, 28, 1835–1851. DOI: 10.1007/s00477-014-0849-8.
- Menafoglio, A., Secchi, P., and Guadagnini, A. (2016), “A Class-kriging Predictor for Functional Compositions With Application to Particle-size Curves in Heterogeneous Aquifers,” Mathematical Geosciences, 48, 463–485. DOI: 10.1007/s11004-015-9625-7.
- Müller, H.-G., Wang, J.-L., and Capra, W. B. (1997), “From Lifetables to Hazard Rates: The Transformation Approach,” Biometrika, 84, 881–892.
- Müller, H.-G., and Yao, F. (2008), “Functional Additive Models,” Journal of the American Statistical Association, 103, 1534–1544. DOI: 10.1198/016214508000000751.
- Panaretos, V. M., and Zemel, Y. (2016), “Amplitude and Phase Variation of Point Processes,” The Annals of Statistics, 44, 771–812. DOI: 10.1214/15-AOS1387.
- Petersen, A., Chen, C.-J., and Müller, H.-G. (2018), “Quantifying and Visualizing Intraregional Connectivity in Resting-State Functional Magnetic Resonance Imaging with Correlation Densities,” Brain Connectivity, 9, 37–47. DOI: 10.1089/brain.2018.0591.
- Petersen, A., and Müller, H.-G. (2016), “Functional Data analysis for Density Functions by Transformation to a Hilbert Space,” Annals of Statistics, 44, 183–218. DOI: 10.1214/15-AOS1363.
- Petersen, A., and Müller, H.-G. (2018), “Fréchet Regression for Random Objects With Euclidean Predictors,” Annals of Statistics, 47, 691–719.
- Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis, Springer Series in Statistics (2nd ed.), New York: Springer.
- Roussas, G. G. (1969), “Nonparametric Estimation of the Transition Distribution Function of a Markov Process,” The Annals of Mathematical Statistics, 40, 1386–1400. DOI: 10.1214/aoms/1177697510.
- Sen, R., and Ma, C. (2015), “Forecasting Density Function: Application in Finance,” Journal of Mathematical Finance, 5, 433. DOI: 10.4236/jmf.2015.55037.
- Talská, R., Menafoglio, A., Machalová, J., Hron, K., and Fišerová, E. (2018), “Compositional Regression With Functional Response,” Computational Statistics & Data Analysis, 123, 66–85. DOI: 10.1016/j.csda.2018.01.018.
- Villani, C. (2003), Topics in Optimal Transportation, Graduate Studies in Mathematics, Vol. 58, American Mathematical Society, Providence, Rhode Island.
- Wang, J.-L., Chiou, J.-M., and Müller, H.-G. (2016), “Functional Data Analysis,” Annual Review of Statistics and its Application, 3, 257–295. DOI: 10.1146/annurev-statistics-041715-033624.
- Yu, K., Park, B. U., and Mammen, E. (2008), “Smooth Backfitting in Generalized Additive Models,” Annals of Statistics, 36, 228–260. DOI: 10.1214/009053607000000596.
- Zhang, X., Park, B. U., and Wang, J.-L. (2013), “Time-varying Additive Models for Longitudinal Data,” Journal of the American Statistical Association, 108, 983–998. DOI: 10.1080/01621459.2013.778776.
- Zhang, Z., and Müller, H.-G. (2011), “Functional Density Synchronization,” Computational Statistics & Data Analysis, 55, 2234–2249. DOI: 10.1016/j.csda.2011.01.007.