Open Access
Issue |
ESAIM: PS
Volume 24, 2020
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Page(s) | 842 - 882 | |
DOI | https://doi.org/10.1051/ps/2020021 | |
Published online | 24 November 2020 |
- R.J. Adler and R. Pyke, Uniform quadratic variation for Gaussian processes. Stochastic Process. Appl. 48 (1993) 191–209 [CrossRef] [Google Scholar]
- J.-M. Azaïs and M. Wschebor, Level sets and Extrema of Random Processes and Fields. John Wiley & Sons, Inc., Hoboken, NJ (2009) [CrossRef] [Google Scholar]
- F. Bachoc, Cross validation and maximum likelihood estimations of hyper-parameters of Gaussian processes with model misspecification. Computat. Stat. Data Anal. 66 (2013) 55–69 [CrossRef] [Google Scholar]
- F. Bachoc, Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes. J. Multivariate Anal. 125 (2014) 1–35 [CrossRef] [Google Scholar]
- F. Bachoc, Asymptotic analysis of covariance parameter estimation for Gaussian processes in the misspecified case. Bernoulli 24 (2018) 1531–1575 [CrossRef] [Google Scholar]
- F. Bachoc and A. Lagnoux, Fixed-domain asymptotic properties of maximum composite likelihood estimators for Gaussian processes. J. Stat. Plann. Inference 209 (2020) 62–75 [CrossRef] [Google Scholar]
- J.M. Bates and C.W. Granger, The combination of forecasts. J. Oper. Res. Soc. 20 (1969) 451–468 [CrossRef] [Google Scholar]
- G. Baxter, A strong limit theorem for Gaussian processes. Proc. Am. Math. Soc. 7 (1956) 522–527 [CrossRef] [Google Scholar]
- Y. Cao and D.J. Fleet, Generalized product of experts for automatic and principled fusion of Gaussian process predictions, in Modern Nonparametrics 3: Automating the Learning Pipeline workshop at NIPS, Montreal. Preprint arXiv:1410.7827 (2014) [Google Scholar]
- I. Clark, Practical Geostatistics, Vol. 3. Applied Science Publishers, London (1979) [Google Scholar]
- J.-F. Coeurjolly, Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. Stat. Inference Stoch. Process. 4 (2001) 199–227 [CrossRef] [MathSciNet] [Google Scholar]
- S. Cohen and J. Istas, Fractional Fields and Applications, With a foreword by Stéphane Jaffard. Vol. 73 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Heidelberg (2013) [Google Scholar]
- N. Cressie, Statistics for Spatial Data. John Wiley (1993) [Google Scholar]
- N. Cressie and D.M. Hawkins, Robust estimation of the variogram: I. J. Int. Assoc. Math. Geol. 12 (1980) 115–125 [CrossRef] [Google Scholar]
- R. Dahlhaus, Efficient parameter estimation for self-similar processes. Ann. Stat. (1989) 1749–1766 [CrossRef] [MathSciNet] [Google Scholar]
- A. Datta, S. Banerjee, A.O. Finley, and A.E. Gelfand, Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets. J. Am. Stat. Assoc. 111 (2016) 800–812 [CrossRef] [PubMed] [Google Scholar]
- I. Daubechies, Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41 (1988) 909–996 [Google Scholar]
- M. David, Geostatistical Ore Reserve Estimation. Elsevier (2012) [Google Scholar]
- M.P. Deisenroth and J.W. Ng, Distributed Gaussian processes, In Proceedings of the 32nd International Conference on Machine Learning, Lille, France. JMLR: W&CP volume 37 (2015) [Google Scholar]
- R. Furrer, M.G. Genton and D. Nychka, Covariance tapering for interpolation of large spatial datasets. J. Comput. Graph. Stat. 15 (2006) 502–523 [CrossRef] [Google Scholar]
- E.G. Gladyšev, A new limit theorem for stochastic processes with Gaussian increments. Teor. Verojatnost. Primenen. 6 (1961) 57–66 [Google Scholar]
- U. Grenander, Abstract inference. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York (1981) [Google Scholar]
- X. Guyon and J. León, Convergence en loi des H-variations d’un processus gaussien stationnaire sur R. Ann. Inst. Henri Poincaré Probab. Statist. 25 (1989) 265–282 [Google Scholar]
- P. Hall, N.I. Fisher and B. Hoffmann, On the nonparametric estimation of covariance functions. Ann. Stat. 22 (1994) 2115–2134 [CrossRef] [Google Scholar]
- P. Hall and P. Patil, Properties of nonparametric estimators of autocovariance for stationary random fields. Probab. Theory Related Fields 99 (1994) 399–424 [CrossRef] [Google Scholar]
- J. Han and X.-P. Zhang, Financial time series volatility analysis using Gaussian process state-space models, in 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE (2015) 358–362 [CrossRef] [Google Scholar]
- J. Hensman and N. Fusi, Gaussian processes for big data. Uncertainty Artif. Intell. (2013) 282–290 [Google Scholar]
- G.E. Hinton, Training products of experts by minimizing contrastive divergence. Neural Computat. 14 (2002) 1771–1800 [CrossRef] [Google Scholar]
- I. Ibragimov and Y. Rozanov, Gaussian Random Processes. Springer-Verlag, New York (1978) [CrossRef] [Google Scholar]
- J. Istas and G. Lang, Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Inst. Henri Poincaré Probab. Statist. 33 (1997) 407–436 [CrossRef] [Google Scholar]
- A. Journel and C. Huijbregts, Mining geostatistics, in Bureau De Recherches Geologiques Et Miniers, France Academic Pres Harcout Brace & Company, Publishers, London, San Diego, New York, Boston, Sidney, Toronto (1978) [Google Scholar]
- C.G. Kaufman, M.J. Schervish, and D.W. Nychka, Covariance tapering for likelihood-based estimation in large spatial data sets. J. Am. Stat. Assoc. 103 (2008) 1545–1555 [CrossRef] [Google Scholar]
- J.T. Kent and A.T.A. Wood, Estimating the fractal dimension of a locally self-similar Gaussian process by using increments. J. Roy. Statist. Soc. Ser. B 59 (1997) 679–699 [Google Scholar]
- S.N. Lahiri, Y. Lee and N. Cressie, On asymptotic distribution and asymptotic efficiency of least squares estimators of spatial variogram parameters. J. Stat. Plann. Inference 103 (2002) 65–85 [CrossRef] [Google Scholar]
- G. Lang and F. Roueff, Semi-parametric estimation of the Hölder exponent of a stationary Gaussian process with minimax rates. Stat. Inference Stoch. Process. 4 (2001) 283–306 [CrossRef] [MathSciNet] [Google Scholar]
- F. Lavancier and P. Rochet. A general procedure to combine estimators. Computat. Stat. Data Anal. 94 (2016) 175–192 [CrossRef] [Google Scholar]
- P. Lévy, Le mouvement brownien plan. Am. J. Math. 62 (1940) 487–550 [CrossRef] [Google Scholar]
- D. Luenberger, Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley (1979) [Google Scholar]
- J. Mateu, E. Porcu, G. Christakos and M. Bevilacqua, Fitting negative spatial covariances to geothermal field temperatures in Nea Kessani (Greece). Environmetrics 18 (2007) 759–773 [CrossRef] [Google Scholar]
- G. Matheron, Traité de géostatistique appliquée, Tome I, Vol. 14 of Editions Technip, Paris. Mémoires du Bureau de Recherches Géologiques et Minières (1962) [Google Scholar]
- E. Pardo-Igúzquiza and P.A. Dowd, AMLE3D: a computer program for the inference of spatial covariance parameters by approximate maximum likelihood estimation. Comput. Geosci. 23 (1997) 793–805 [CrossRef] [Google Scholar]
- O. Perrin, Quadratic variation for Gaussian processes and application to time deformation. Stochastic Process. Appl. 82 (1999) 293–305 [CrossRef] [Google Scholar]
- G. Pólya, Remarks on characteristic functions, in Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability, August 13–18, 1945 and January 27–29, 1946, edited by J. Neyman. Statistical Laboratory of the University of California, Berkeley. University of California Press, Berkeley, CA (1949) 115–123 [Google Scholar]
- C. Rasmussen and C. Williams, Gaussian Processes for Machine Learning. The MIT Press, Cambridge (2006) [Google Scholar]
- F. Richard, Anisotropy of Hölder Gaussian random fields: characterization, estimation, and application to image textures. Stat. Comput. 28 (2018) 1155–1168 [CrossRef] [Google Scholar]
- F. Richard and H. Biermé, Statistical tests of anisotropy for fractional Brownian textures. application to full-field digital mammography. J. Math. Imaging Vis. 36 (2010) 227–240 [CrossRef] [Google Scholar]
- L. Risser, F. Vialard, R. Wolz, M. Murgasova, D. Holm and D. Rueckert, ADNI: Simultaneous multiscale registration using large deformation diffeomorphic metric mapping. IEEE Trans. Med. Imaging 30 (2011) 1746–1759 [CrossRef] [PubMed] [Google Scholar]
- O. Roustant, D. Ginsbourger and Y. Deville, DiceKriging, DiceOptim: two R packages for the analysis of computer experiments by Kriging-based metamodeling and optimization. J. Stat. Softw. 51 (2012) [CrossRef] [Google Scholar]
- H. Rue and L. Held, Gaussian Markov Random Fields Theory and Applications. Chapman & Hall (2005) [CrossRef] [Google Scholar]
- D. Rullière, N. Durrande, F. Bachoc and C. Chevalier, Nested Kriging predictions for datasets with a large number of observations. Stat. Comput. 28 (2018) 849–867 [CrossRef] [Google Scholar]
- G. Samorodnitsky and M. Taqqu, Non-Gaussian Stable Processes: Stochastic Models with Infinite Variance. Chapman ft Hall, London (1994) [Google Scholar]
- T.J. Santner, B.J. Williams and W.I. Notz, The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer-Verlag, New York (2003) [CrossRef] [Google Scholar]
- D. Slepian, On the zeros of Gaussian noise, in Proc. Sympos. Time Series Analysis (Brown Univ., 1962). Wiley, New York (1963) 104–115 [Google Scholar]
- M. Stein, Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York (1999) [CrossRef] [Google Scholar]
- M.L. Stein, Limitations on low rank approximations for covariance matrices of spatial data. Spatial Stat. 8 (2014) 1–19 [CrossRef] [Google Scholar]
- M.L. Stein, Z. Chi and L.J. Welty, Approximating likelihoods for large spatial data sets. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.) 66 (2004) 275–296 [CrossRef] [Google Scholar]
- V. Tresp, A Bayesian committee machine. Neural Computat. 12 (2000) 2719–2741 [CrossRef] [Google Scholar]
- B. van Stein, H. Wang, W. Kowalczyk, T. Bäck and M. Emmerich, Optimally weighted cluster Kriging for big data regression, in International Symposium on Intelligent Data Analysis . Springer (2015) 310–321 [Google Scholar]
- C. Varin, N. Reid and D. Firth, An overview of composite likelihood methods. Stat. Sinica 21 (2011) 5–42 [Google Scholar]
- A.V. Vecchia, Estimation and model identification for continuous spatial processes. J. Roy. Stat. Soc.: Ser. B (Methodological) 50 (1988) 297–312 [Google Scholar]
- Y. Wu, J.M. Hernández-Lobato and Z. Ghahramani, Gaussian process volatility model, in Advances in Neural Information Processing Systems 27, edited by Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence and K.Q. Weinberger. Curran Associates Inc. (2014) 1044–1052 [Google Scholar]
- H. Zhang and Y. Wang, Kriging and cross-validation for massive spatial data. Environmetrics 21 (2010) 290–304 [CrossRef] [Google Scholar]
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