References
- Anderes, E., and Chatterjee, S. (2009), “Consistent Estimates of Deformed Isotropic Gaussian Random Fields on the Plane,” The Annals of Statistics, 37, 2324–2350. DOI: https://doi.org/10.1214/08-AOS647.
- Anderes, E. B., and Stein, M. L. (2008), “Estimating Deformations of Isotropic Gaussian Random Fields on the Plane,” The Annals of Statistics, 36, 719–741. DOI: https://doi.org/10.1214/009053607000000893.
- Birchfield, S. T., and Subramanya, A. (2005), “Microphone Array Position Calibration by Basis-Point Classical Multidimensional Scaling,” IEEE Transactions on Speech and Audio Processing, 13, 1025–1034. DOI: https://doi.org/10.1109/TSA.2005.851893.
- Bornn, L., Shaddick, G., and Zidek, J. V. (2012), “Modeling Nonstationary Processes Through Dimension Expansion,” Journal of the American Statistical Association, 107, 281–289. DOI: https://doi.org/10.1080/01621459.2011.646919.
- Calder, C. A. (2008), “A Dynamic Process Convolution Approach to Modeling Ambient Particulate Matter Concentrations,” Environmetrics, 19, 39–48. DOI: https://doi.org/10.1002/env.852.
- Cressie, N. (1993), Statistics for Spatial Data, New York: Wiley.
- Damian, D., Sampson, P. D., and Guttorp, P. (2001), “Bayesian Estimation of Semi-Parametric Non-Stationary Spatial Covariance Structures,” Environmetrics, 12, 161–178. DOI: https://doi.org/10.1002/1099-095X(200103)12:2<161::AID-ENV452>3.0.CO;2-G.
- Deutsch, C. V. (1997), “Direct Assessment of Local Accuracy and Precision,” Geostatistics Wollongong, 96, 115–125.
- Fouedjio, F. (2017), “Second-Order Non-Stationary Modeling Approaches for Univariate Geostatistical Data,” Stochastic Environmental Research and Risk Assessment, 31, 1887–1906. DOI: https://doi.org/10.1007/s00477-016-1274-y.
- Fouedjio, F., Desassis, N., and Rivoirard, J. (2016), “A Generalized Convolution Model and Estimation for Non-Stationary Random Functions,” Spatial Statistics, 16, 35–52. DOI: https://doi.org/10.1016/j.spasta.2016.01.002.
- Fouedjio, F., Desassis, N., and Romary, T. (2015), “Estimation of Space Deformation Model for Non-Stationary Random Functions,” Spatial Statistics, 13, 45–61. DOI: https://doi.org/10.1016/j.spasta.2015.05.001.
- Fouedjio, F., and Klump, J. (2019), “Exploring Prediction Uncertainty of Spatial Data in Geostatistical and Machine Learning Approaches,” Environmental Earth Sciences, 78, 38. DOI: https://doi.org/10.1007/s12665-018-8032-z.
- Fuentes, M. (2002), “Spectral Methods for Nonstationary Spatial Processes,” Biometrika, 89, 197–210.
- Fuentes, M., and Smith, R. L. (2001), “A New Class of Nonstationary Spatial Models,” Technical Report, North Carolina State University, Department of Statistics.
- Fuglstad, G.-A., Lindgren, F., Simpson, D., and Rue, H. (2015), “Exploring a New Class of Non-Stationary Spatial Gaussian Random Fields With Varying Local Anisotropy,” Statistica Sinica, 25, 115–133.
- Fuglstad, G.-A., Simpson, D., Lindgren, F., and Rue, H. (2015), “Does Non-Stationary Spatial Data Always Require Non-Stationary Random Fields?,” Spatial Statistics, 14, 505–531. DOI: https://doi.org/10.1016/j.spasta.2015.10.001.
- Genton, M. G., and Kleiber, W. (2015), “Cross-Covariance Functions for Multivariate Geostatistics,” Statistical Science, 30, 147–163. DOI: https://doi.org/10.1214/14-STS487.
- Gneiting, T., and Raftery, A. E. (2007), “Strictly Proper Scoring Rules, Prediction, and Estimation,” Journal of the American Statistical Association, 102, 359–378. DOI: https://doi.org/10.1198/016214506000001437.
- Goovaerts, P. (2001), “Geostatistical Modelling of Uncertainty in Soil Science,” Geoderma, 103, 3–26. DOI: https://doi.org/10.1016/S0016-7061(01)00067-2.
- Guan, Y., Sampson, C., Tucker, J. D., Chang, W., Mondal, A., Haran, M., and Sulsky, D. (2019), “Computer Model Calibration Based on Image Warping Metrics: An Application for Sea Ice Deformation,” Journal of Agricultural, Biological and Environmental Statistics, 24, 444– 463. DOI: https://doi.org/10.1007/s13253-019-00353-7.
- Guttorp, P., and Gneiting, T. (2006), “Studies in the History of Probability and Statistics XLIX: On the Matérn Correlation Family,” Biometrika, 93, 989–995. DOI: https://doi.org/10.1093/biomet/93.4.989.
- Haas, T. C. (1990a), “Kriging and Automated Variogram Modeling Within a Moving Window,” Atmospheric Environment. Part A. General Topics, 24, 1759–1769. DOI: https://doi.org/10.1016/0960-1686(90)90508-K.
- Haas, T. C. (1990b), “Lognormal and Moving Window Methods of Estimating Acid Deposition,” Journal of the American Statistical Association, 85, 950–963.
- Heaton, M. J., Christensen, W. F., and Terres, M. A. (2017), “Nonstationary Gaussian Process Models Using Spatial Hierarchical Clustering From Finite Differences,” Technometrics, 59, 93–101. DOI: https://doi.org/10.1080/00401706.2015.1102763.
- Higdon, D. (1998), “A Process-Convolution Approach to Modelling Temperatures in the North Atlantic Ocean,” Environmental and Ecological Statistics, 5, 173–190.
- Higdon, D., Swall, J., and Kern, J. (1999), “Non-Stationary Spatial Modeling,” Bayesian Statistics, 6, 761–768.
- Iovleff, S., and Perrin, O. (2004), “Estimating a Nonstationary Spatial Structure Using Simulated Annealing,” Journal of Computational and Graphical Statistics, 13, 90–105. DOI: https://doi.org/10.1198/1061860043100.
- Ji, X., and Zha, H. (2004), “Sensor Positioning in Wireless Ad-Hoc Sensor Networks Using Multidimensional Scaling,” in IEEE INFOCOM 2004 (Vol. 4), IEEE, pp. 2652–2661.
- Kahle, D., and Wickham, H. (2013), “ggmap: Spatial Visualization With ggplot2,” The R Journal, 5, 144–161. DOI: https://doi.org/10.32614/RJ-2013-014.
- Kleiber, W. (2016), “High Resolution Simulation of Nonstationary Gaussian Random Fields,” Computational Statistics & Data Analysis, 101, 277–288.
- Kurtek, S. A., Srivastava, A., and Wu, W. (2011), “Signal Estimation Under Random Time-Warpings and Nonlinear Signal Alignment,” in Advances in Neural Information Processing Systems, pp. 675–683.
- Kurtek, S. A., Wu, W., Christensen, G. E., and Srivastava, A. (2013), “Segmentation, Alignment and Statistical Analysis of Biosignals With Application to Disease Classification,” Journal of Applied Statistics, 40, 1270–1288. DOI: https://doi.org/10.1080/02664763.2013.785492.
- Lahiri, S., Robinson, D., and Klassen, E. (2015), “Precise Matching of PL Curves in RN in the Square Root Velocity Framework,” Geometry, Imaging and Computing, 2, 133–186.
- Li, Y., and Sun, Y. (2019), “Efficient Estimation of Nonstationary Spatial Covariance Functions With Application to High-Resolution Climate Model Emulation,” Statistica Sinica, 29, 1209–1231.
- Lindgren, F., Rue, H., and Lindström, J. (2011), “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach,” Journal of the Royal Statistical Society, Series B, 73, 423–498. DOI: https://doi.org/10.1111/j.1467-9868.2011.00777.x.
- Lloyd, C. D., and Atkinson, P. M. (2000), “Interpolating Elevation With Locally-Adaptive Kriging,” Innovations in GIS, 7, 241–253.
- Lloyd, C. D., and Atkinson, P. M. (2002), “Non-Stationary Approaches for Mapping Terrain and Assessing Prediction Uncertainty,” Transactions in GIS, 6, 17–30.
- Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979), Multivariate Analysis, London: Academic Press.
- Marron, J. S., Ramsay, J. O., Sangalli, L. M., and Srivastava, A. (2015), “Functional Data Analysis of Amplitude and Phase Variation,” Statistical Science, 30, 468–484. DOI: https://doi.org/10.1214/15-STS524.
- Matérn, B. (1986), Spatial Variation (2nd ed.), Berlin: Springer-Verlag.
- Meng, R., Saade, S., Kurtek, S., Berger, B., Brien, C., Pillen, K., Tester, M., and Sun, Y. (2017), “Growth Curve Registration for Evaluating Salinity Tolerance in Barley,” Plant Methods, 13, 18. DOI: https://doi.org/10.1186/s13007-017-0165-7.
- Moyeed, R. A., and Papritz, A. (2002), “An Empirical Comparison of Kriging Methods for Nonlinear Spatial Point Prediction,” Mathematical Geology, 34, 365–386.
- Nychka, D., Hammerling, D., Krock, M., and Wiens, A. (2018), “Modeling and Emulation of Nonstationary Gaussian Fields,” Spatial Statistics, 28, 21–38. DOI: https://doi.org/10.1016/j.spasta.2018.08.006.
- Nychka, D., and Saltzman, N. (1998), “Design of Air-Quality Monitoring Networks,” in Case Studies in Environmental Statistics, eds. D. Nychka, W. W. Piegorsch, and L. H. Cox, New York: Springer, pp. 51–76.
- Nychka, D., Wikle, C., and Royle, J. A. (2002), “Multiresolution Models for Nonstationary Spatial Covariance Functions,” Statistical Modelling, 2, 315–331. DOI: https://doi.org/10.1191/1471082x02st037oa.
- Paciorek, C. J., and Schervish, M. J. (2006), “Spatial Modelling Using a New Class of Nonstationary Covariance Functions,” Environmetrics, 17, 483–506. DOI: https://doi.org/10.1002/env.785.
- Reich, B. J., Eidsvik, J., Guindani, M., Nail, A. J., and Schmidt, A. M. (2011), “A Class of Covariate-Dependent Spatiotemporal Covariance Functions,” The Annals of Applied Statistics, 5, 2265–2687. DOI: https://doi.org/10.1214/11-AOAS482.
- Risser, M. D. (2016), “Nonstationary Spatial Modeling, With Emphasis on Process Convolution and Covariate-Driven Approaches,” arXiv no. 1610.02447.
- Robinson, D. T. (2012), Functional Data Analysis and Partial Shape Matching in the Square Root Velocity Framework, Ph.D. thesis, Florida State University.
- Samir, C., Kurtek, S., Srivastava, A., and Borges, N. (2016), “An Elastic Functional Data Analysis Framework for Preoperative Evaluation of Patients With Rheumatoid Arthritis,” in 2016 IEEE Winter Conference on Applications of Computer Vision (WACV), IEEE, pp. 1–8. DOI: https://doi.org/10.1109/WACV.2016.7477602.
- Sampson, P. D., and Guttorp, P. (1992), “Nonparametric Estimation of Nonstationary Spatial Covariance Structure,” Journal of the American Statistical Association, 87, 108–119. DOI: https://doi.org/10.1080/01621459.1992.10475181.
- Schmidt, A. M., and O’Hagan, A. (2003), “Bayesian Inference for Non-Stationary Spatial Covariance Structure via Spatial Deformations,” Journal of the Royal Statistical Society, Series B, 65, 743–758. DOI: https://doi.org/10.1111/1467-9868.00413.
- Srivastava, A., and Klassen, E. P. (2016), Functional and Shape Data Analysis, New York: Springer.
- Srivastava, A., Wu, W., Kurtek, S., Klassen, E., and Marron, J. S. (2011), “Registration of Functional Data Using Fisher-Rao Metric,” arXiv no. 1103.3817.
- Stephenson, J., Holmes, C., Gallagher, K., and Pintore, A. (2005), “A Statistical Technique for Modelling Non-Stationary Spatial Processes,” in Geostatistics Banff 2004, eds. O. Leuangthong, and C. V. Deutsch, Dordrecht: Springer Netherlands, pp. 125–134.
- Torgerson, W. S. (1958), Theory and Methods of Scaling, New York: Wiley.
- Tucker, J. D. (2020), “fdasrvf: Elastic Functional Data Analysis,” R Package Version 1.9.3.
- Tucker, J. D., Wu, W., and Srivastava, A. (2013), “Generative Models for Functional Data Using Phase and Amplitude Separation,” Computational Statistics & Data Analysis, 61, 50–66.