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Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics

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  1. Rajala, T. & Penttinen, A., 2014. "Bayesian analysis of a Gibbs hard-core point pattern model with varying repulsion range," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 530-541.
  2. May, Paul & Biesecker, Matthew & Rekabdarkolaee, Hossein Moradi, 2022. "Response envelopes for linear coregionalization models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
  3. Marrel, Amandine & Iooss, Bertrand, 2024. "Probabilistic surrogate modeling by Gaussian process: A review on recent insights in estimation and validation," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
  4. Liu, Haibin & Davidson, Rachel A. & Apanasovich, Tatiyana V., 2008. "Spatial generalized linear mixed models of electric power outages due to hurricanes and ice storms," Reliability Engineering and System Safety, Elsevier, vol. 93(6), pages 897-912.
  5. Tamara Cantú Maltauro & Miguel Angel Uribe-Opazo & Luciana Pagliosa Carvalho Guedes & Manuel Galea & Orietta Nicolis, 2025. "Spatial–Temporal Variability of Soybean Yield Using Separable Covariance Structure," Agriculture, MDPI, vol. 15(11), pages 1-21, May.
  6. Qian Ren & Sudipto Banerjee, 2013. "Hierarchical Factor Models for Large Spatially Misaligned Data: A Low-Rank Predictive Process Approach," Biometrics, The International Biometric Society, vol. 69(1), pages 19-30, March.
  7. Sierra Pugh & Matthew J. Heaton & Jeff Svedin & Neil Hansen, 2019. "Spatiotemporal Lagged Models for Variable Rate Irrigation in Agriculture," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 634-650, December.
  8. Arafat, Ahmed & Porcu, Emilio & Bevilacqua, Moreno & Mateu, Jorge, 2018. "Equivalence and orthogonality of Gaussian measures on spheres," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 306-318.
  9. Varin, Cristiano & Host, Gudmund & Skare, Oivind, 2005. "Pairwise likelihood inference in spatial generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1173-1191, June.
  10. Matthew J. Heaton & Stephan R. Sain & Andrew J. Monaghan & Olga V. Wilhelmi & Mary H. Hayden, 2015. "An Analysis of an Incomplete Marked Point Pattern of Heat-Related 911 Calls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 123-135, March.
  11. Monterrubio-Gómez, Karla & Roininen, Lassi & Wade, Sara & Damoulas, Theodoros & Girolami, Mark, 2020. "Posterior inference for sparse hierarchical non-stationary models," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
  12. Tingjin Chu & Jialuo Liu & Jun Zhu & Haonan Wang, 2022. "Spatio-Temporal Expanding Distance Asymptotic Framework for Locally Stationary Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 689-713, August.
  13. Hamid Zareifard & Majid Jafari Khaledi, 2025. "Skew Gaussian Markov Random Fields Under Decomposable Graphs," Environmetrics, John Wiley & Sons, Ltd., vol. 36(6), September.
  14. Bevilacqua, Moreno & Caamaño-Carrillo, Christian & Porcu, Emilio, 2022. "Unifying compactly supported and Matérn covariance functions in spatial statistics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
  15. Lim, Chae Young & Chen, Chien-Hung & Wu, Wei-Ying, 2017. "Numerical instability of calculating inverse of spatial covariance matrices," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 182-188.
  16. Anderes, Ethan B. & Stein, Michael L., 2011. "Local likelihood estimation for nonstationary random fields," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 506-520, March.
  17. Ghulam A. Qadir & Ying Sun, 2021. "Semiparametric estimation of cross‐covariance functions for multivariate random fields," Biometrics, The International Biometric Society, vol. 77(2), pages 547-560, June.
  18. ShengLi Tzeng & Bo-Yu Chen & Hsin-Cheng Huang, 2024. "Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(2), pages 301-319, June.
  19. Zhang, Tonglin, 2017. "An example of inconsistent MLE of spatial covariance parameters under increasing domain asymptotics," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 108-113.
  20. Lu, Zudi & Tjostheim, Dag & Yao, Qiwei, 2008. "Spatial smoothing, Nugget effect and infill asymptotics," LSE Research Online Documents on Economics 24133, London School of Economics and Political Science, LSE Library.
  21. Veronica J. Berrocal & Alan E. Gelfand & David M. Holland, 2012. "Space-Time Data fusion Under Error in Computer Model Output: An Application to Modeling Air Quality," Biometrics, The International Biometric Society, vol. 68(3), pages 837-848, September.
  22. Girard, Didier A., 2016. "Asymptotic near-efficiency of the “Gibbs-energy and empirical-variance” estimating functions for fitting Matérn models — I: Densely sampled processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 191-197.
  23. Korte-Stapff, Moritz & Karvonen, Toni & Moulines, Éric, 2025. "Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
  24. Furrer, Reinhard & Hediger, Michael, 2024. "On the orthogonality of zero-mean Gaussian measures: Sufficiently dense sampling," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
  25. De Oliveira, Victor & Kone, Bazoumana, 2015. "Prediction intervals for integrals of Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 37-51.
  26. Ninna Vihrs & Jesper Møller & Alan E. Gelfand, 2022. "Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 185-210, March.
  27. Minhee Kim & Todd Allen & Kaibo Liu, 2023. "Covariate Dependent Sparse Functional Data Analysis," INFORMS Joural on Data Science, INFORMS, vol. 2(1), pages 81-98, April.
  28. Jaewoo Park & Sangwan Lee, 2022. "A projection‐based Laplace approximation for spatial latent variable models," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
  29. Peter J. Diggle & Emanuele Giorgi, 2016. "Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1096-1120, July.
  30. Sujit K. Sahu & Alan E. Gelfand & David M. Holland, 2010. "Fusing point and areal level space–time data with application to wet deposition," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 77-103, January.
  31. Bachoc, François & Lagnoux, Agnès & Nguyen, Thi Mong Ngoc, 2017. "Cross-validation estimation of covariance parameters under fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 42-67.
  32. Sabyasachi Mukhopadhyay & Joseph O. Ogutu & Gundula Bartzke & Holly T. Dublin & Hans-Peter Piepho, 2019. "Modelling Spatio-Temporal Variation in Sparse Rainfall Data Using a Hierarchical Bayesian Regression Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 369-393, June.
  33. David L. Miller & Richard Glennie & Andrew E. Seaton, 2020. "Understanding the Stochastic Partial Differential Equation Approach to Smoothing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 1-16, March.
  34. Bachoc, François, 2013. "Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 55-69.
  35. Guinness, Joseph & Fuentes, Montserrat, 2016. "Isotropic covariance functions on spheres: Some properties and modeling considerations," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 143-152.
  36. Mahmoud, Hamdy F.F. & Kim, Inyoung, 2019. "Semiparametric spatial mixed effects single index models," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 108-122.
  37. Wu, Wei-Ying & Lim, Chae Young & Xiao, Yimin, 2013. "Tail estimation of the spectral density for a stationary Gaussian random field," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 74-91.
  38. Jorge Castillo-Mateo & Miguel Lafuente & Jesús Asín & Ana C. Cebrián & Alan E. Gelfand & Jesús Abaurrea, 2022. "Spatial Modeling of Day-Within-Year Temperature Time Series: An Examination of Daily Maximum Temperatures in Aragón, Spain," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 487-505, September.
  39. G. Tamagny & M. Ribatet, 2025. "Spatial Modeling of Extremes and an Angular Component," Environmetrics, John Wiley & Sons, Ltd., vol. 36(6), September.
  40. Giovanna Jona Lasinio & Gianluca Mastrantonio & Alessio Pollice, 2013. "Discussing the “big n problem”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 97-112, March.
  41. Federico Blasi & Reinhard Furrer, 2025. "A Class of Modular and Flexible Covariate‐Based Covariance Functions for Nonstationary Spatial Modeling," Environmetrics, John Wiley & Sons, Ltd., vol. 36(8), December.
  42. Rowland G. Seymour & Theodore Kypraios & Philip D. O’Neill & Thomas J. Hagenaars, 2021. "A Bayesian nonparametric analysis of the 2003 outbreak of highly pathogenic avian influenza in the Netherlands," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1323-1343, November.
  43. Lecomte, J.B. & Benoît, H.P. & Etienne, M.P. & Bel, L. & Parent, E., 2013. "Modeling the habitat associations and spatial distribution of benthic macroinvertebrates: A hierarchical Bayesian model for zero-inflated biomass data," Ecological Modelling, Elsevier, vol. 265(C), pages 74-84.
  44. Denis Allard & Lucia Clarotto & Thomas Opitz & Thomas Romary, 2021. "Discussion on “Competition on Spatial Statistics for Large Datasets”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 604-611, December.
  45. Hong, Yiping & Zhou, Zaiying & Yang, Ying, 2020. "Hypothesis testing for the smoothness parameter of Matérn covariance model on a regular grid," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
  46. Paritosh Kumar Roy & Alexandra M. Schmidt, 2025. "A Comparison of Bayesian Approximation Methods for Analyzing Large Spatial Skewed Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(4), pages 1094-1110, December.
  47. Wenpin Tang & Lu Zhang & Sudipto Banerjee, 2021. "On identifiability and consistency of the nugget in Gaussian spatial process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 1044-1070, November.
  48. Arthur P. Guillaumin & Adam M. Sykulski & Sofia C. Olhede & Frederik J. Simons, 2022. "The Debiased Spatial Whittle likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1526-1557, September.
  49. Becky Tang & Henry A. Frye & Alan E. Gelfand & John A. Silander, 2023. "Zero-Inflated Beta Distribution Regression Modeling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 117-137, March.
  50. Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.
  51. Paciorek, Christopher J., 2007. "Computational techniques for spatial logistic regression with large data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3631-3653, May.
  52. James S. Martin & David J. Murrell & Sofia C. Olhede, 2023. "Multivariate geometric anisotropic Cox processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1420-1465, September.
  53. Matthew Heiner & Athanasios Kottas, 2022. "Autoregressive density modeling with the Gaussian process mixture transition distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 157-177, March.
  54. Soumyakanti Pan & Sudipto Banerjee, 2026. "Bayesian Inference for Spatially‐Temporally Misaligned Data Using Predictive Stacking," Environmetrics, John Wiley & Sons, Ltd., vol. 37(2), March.
  55. Lu, Zudi & Tjøstheim, Dag & Yao, Qiwei, 2008. "Spatial smoothing, Nugget effect and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3145-3151, December.
  56. Christopher J. Geoga & Mihai Anitescu & Michael L. Stein, 2021. "Flexible nonstationary spatiotemporal modeling of high‐frequency monitoring data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
  57. Huang, H.-C. & Martinez, F. & Mateu, J. & Montes, F., 2007. "Model comparison and selection for stationary space-time models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4577-4596, May.
  58. Tarik Faouzi & Emilio Porcu & Igor Kondrashuk & Moreno Bevilacqua, 2024. "Convergence arguments to bridge cauchy and matérn covariance functions," Statistical Papers, Springer, vol. 65(2), pages 645-660, April.
  59. Keshavarz, Hossein & Scott, Clayton & Nguyen, XuanLong, 2016. "On the consistency of inversion-free parameter estimation for Gaussian random fields," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 245-266.
  60. Bolin, David & Lindgren, Finn, 2013. "A comparison between Markov approximations and other methods for large spatial data sets," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 7-21.
  61. Ganggang Xu & Marc G. Genton, 2017. "Tukey -and- Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1236-1249, July.
  62. Colin Lewis-Beck & Zhengyuan Zhu & Victoria Walker & Brian Hornbuckle, 2020. "Modeling Crop Phenology in the US Corn Belt Using Spatially Referenced SMOS Satellite Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 657-675, December.
  63. Philip A. White & Alan E. Gelfand, 2021. "Multivariate functional data modeling with time-varying clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 586-602, September.
  64. Werner Müller & Milan Stehlík, 2009. "Issues in the optimal design of computer simulation experiments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 163-177, March.
  65. Eric Yanchenko & Howard D. Bondell & Brian J. Reich, 2024. "Spatial regression modeling via the R2D2 framework," Environmetrics, John Wiley & Sons, Ltd., vol. 35(2), March.
  66. Jonas Wallin & David Bolin, 2015. "Geostatistical Modelling Using Non-Gaussian Matérn Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 872-890, September.
  67. Zih‐Bing Chen & Hao‐Yun Huang & Cheng‐Xin Yang, 2025. "Comparative Analysis of Bootstrap Techniques for Confidence Interval Estimation in Spatial Covariance Parameters With Large Spatial Data," Environmetrics, John Wiley & Sons, Ltd., vol. 36(3), April.
  68. Didem Kochan & Xiu Yang, 2025. "Gaussian Process Regression with Soft Equality Constraints," Mathematics, MDPI, vol. 13(3), pages 1-17, January.
  69. Moreno Bevilacqua & Ronny Vallejos & Daira Velandia, 2015. "Assessing the significance of the correlation between the components of a bivariate Gaussian random field," Environmetrics, John Wiley & Sons, Ltd., vol. 26(8), pages 545-556, December.
  70. R. S. Fagundes & M. A. Uribe-Opazo & M. Galea & L. P. C. Guedes, 2018. "Spatial Variability in Slash Linear Modeling with Finite Second Moment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 276-296, June.
  71. Philip A. White & Durban G. Keeler & Daniel Sheanshang & Summer Rupper, 2022. "Improving piecewise linear snow density models through hierarchical spatial and orthogonal functional smoothing," Environmetrics, John Wiley & Sons, Ltd., vol. 33(5), August.
  72. Benjamin M. Taylor & Ricardo Andrade‐Pacheco & Hugh J. W. Sturrock, 2018. "Continuous inference for aggregated point process data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1125-1150, October.
  73. Gelfand, Alan E. & Banerjee, Sudipto & Sirmans, C.F. & Tu, Yong & Eng Ong, Seow, 2007. "Multilevel modeling using spatial processes: Application to the Singapore housing market," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3567-3579, April.
  74. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.
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  76. Zhou, Yuzhen & Xiao, Yimin, 2018. "Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 56-72.
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  79. Ip, Ryan H.L. & Li, W.K., 2017. "A class of valid Matérn cross-covariance functions for multivariate spatio-temporal random fields," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 115-119.
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