{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T11:35:19Z","timestamp":1774611319534,"version":"3.50.1"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,9,24]],"date-time":"2013-09-24T00:00:00Z","timestamp":1379980800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1007\/s10957-013-0423-4","type":"journal-article","created":{"date-parts":[[2013,9,23]],"date-time":"2013-09-23T20:52:12Z","timestamp":1379969532000},"page":"888-911","source":"Crossref","is-referenced-by-count":3,"title":["Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context"],"prefix":"10.1007","volume":"167","author":[{"given":"M. D.","family":"Ruiz-Medina","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V. V.","family":"Anh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. M.","family":"Espejo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. M.","family":"Angulo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. P.","family":"Fr\u00edas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,9,24]]},"reference":[{"key":"423_CR1","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/1010093","volume":"10","author":"B. Mandelbrot","year":"1968","unstructured":"Mandelbrot, B., Van Ness, J.W.: Fractional Brownian motion, fractional noises and applications. SIAM Rev. 10, 422\u2013437 (1968)","journal-title":"SIAM Rev."},{"key":"423_CR2","doi-asserted-by":"crossref","first-page":"19","DOI":"10.4171\/RMI\/217","volume":"13","author":"A. Benassi","year":"1997","unstructured":"Benassi, A., Jaffard, S., Roux, D.: Elliptic Gaussian random processes. Rev. Mat. Iberoam. 13, 19\u201390 (1997)","journal-title":"Rev. Mat. Iberoam."},{"key":"423_CR3","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1023\/A:1009901714819","volume":"3","author":"A. Ayache","year":"2000","unstructured":"Ayache, A., L\u00e9vy-V\u00e9hel, J.: The generalized multifractional Brownian motion. Stat. Inference Stoch. Process. 3, 7\u201318 (2000)","journal-title":"Stat. Inference Stoch. Process."},{"key":"423_CR4","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s004400050224","volume":"114","author":"S. Jaffard","year":"1999","unstructured":"Jaffard, S.: The multifractal nature of L\u00e9vy processes. Probab. Theory Relat. Fields 114, 207\u2013227 (1999)","journal-title":"Probab. Theory Relat. Fields"},{"key":"423_CR5","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1081\/SAP-120030456","volume":"22","author":"M.D. Ruiz-Medina","year":"2004","unstructured":"Ruiz-Medina, M.D., Anh, V.V., Angulo, J.M.: Fractional generalized random fields of variable order. Stoch. Anal. Appl. 22, 775\u2013800 (2004)","journal-title":"Stoch. Anal. Appl."},{"key":"423_CR6","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1023\/A:1010474332598","volume":"104","author":"V.V. Anh","year":"2001","unstructured":"Anh, V.V., Leonenko, N.N.: Spectral analysis of fractional kinetic equations with random data. J. Stat. Phys. 104, 1349\u20131387 (2001)","journal-title":"J. Stat. Phys."},{"key":"423_CR7","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1239\/aap\/1113402402","volume":"37","author":"M. Kelbert","year":"2005","unstructured":"Kelbert, M., Leonenko, N.N., Ruiz-Medina, M.D.: Fractional random fields associated with stochastic fractional heat equations. Adv. Appl. Probab. 37, 108\u2013133 (2005)","journal-title":"Adv. Appl. Probab."},{"key":"423_CR8","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1214\/EJP.v16-891","volume":"16","author":"N.N. Leonenko","year":"2011","unstructured":"Leonenko, N.N., Ruiz-Medina, M.D., Taqqu, M.: Fractional elliptic, hyperbolic and parabolic random fields. Electron. J. Probab. 16, 1134\u20131172 (2011)","journal-title":"Electron. J. Probab."},{"key":"423_CR9","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/S0378-3758(03)00136-8","volume":"123","author":"V. Anh","year":"2004","unstructured":"Anh, V., Leonenko, N.N., Sakhno, L.M.: On a class of minimum contrast estimators for fractional stochastic processes and fields. J. Stat. Plan. Inference 123, 161\u2013185 (2004)","journal-title":"J. Stat. Plan. Inference"},{"key":"423_CR10","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1016\/j.jspi.2006.03.001","volume":"137","author":"V. Anh","year":"2007","unstructured":"Anh, V., Leonenko, N.N., Sakhno, L.M.: Minimum contrast estimation of random processes based on information of second and third orders. J. Stat. Plan. Inference 137, 1302\u20131331 (2007)","journal-title":"J. Stat. Plan. Inference"},{"key":"423_CR11","volume-title":"Modern Spatiotemporal Geostatistics","author":"G. Christakos","year":"2000","unstructured":"Christakos, G.: Modern Spatiotemporal Geostatistics. Oxford University Press, New York (2000)"},{"key":"423_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8877-5","volume-title":"Asymptotic Theory of Nonlinear Regression","author":"A.V. Ivanov","year":"1997","unstructured":"Ivanov, A.V.: Asymptotic Theory of Nonlinear Regression. Kluwer, Dordrecht (1997)"},{"key":"423_CR13","series-title":"Mathematics and Its Applications","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-4607-4","volume-title":"Limit Theorems for Random Fields with Singular Spectrum","author":"N.N. Leonenko","year":"1999","unstructured":"Leonenko, N.N.: Limit Theorems for Random Fields with Singular Spectrum. Mathematics and Its Applications, vol. 465. Kluwer, Dordrecht (1999)"},{"key":"423_CR14","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/S0047-259X(02)00024-6","volume":"85","author":"M.D. Ruiz-Medina","year":"2003","unstructured":"Ruiz-Medina, M.D., Angulo, J.M., Anh, V.V.: Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields. J. Multivar. Anal. 85, 192\u2013216 (2003)","journal-title":"J. Multivar. Anal."},{"key":"423_CR15","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1016\/j.jmva.2005.10.006","volume":"97","author":"R. Fern\u00e1ndez-Pascual","year":"2006","unstructured":"Fern\u00e1ndez-Pascual, R., Ruiz-Medina, M.D., Angulo, J.M.: Estimation of intrinsic processes affected by additive fractal noise. J. Multivar. Anal. 97, 1361\u20131381 (2006)","journal-title":"J. Multivar. Anal."},{"key":"423_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1154-9","volume-title":"Linear Processes in Function Spaces","author":"D. Bosq","year":"2000","unstructured":"Bosq, D.: Linear Processes in Function Spaces. Springer, New York (2000)"},{"key":"423_CR17","doi-asserted-by":"crossref","DOI":"10.1002\/9780470724033","volume-title":"Inference and Predictions in Large Dimensions","author":"D. Bosq","year":"2007","unstructured":"Bosq, D., Blanke, D.: Inference and Predictions in Large Dimensions. Wiley, Paris (2007)"},{"key":"423_CR18","first-page":"230","volume":"102","author":"M.D. Ruiz-Medina","year":"2011","unstructured":"Ruiz-Medina, M.D.: Spatial autoregressive and moving average Hilbertian processes. J. Multivar. Anal. 102, 230\u2013292 (2011)","journal-title":"J. Multivar. Anal."},{"key":"423_CR19","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1002\/env.1143","volume":"23","author":"M.D. Ruiz-Medina","year":"2012","unstructured":"Ruiz-Medina, M.D.: Spatial functional prediction from spatial autoregressive Hilbertian processes. Environmetrics 23, 119\u2013128 (2012)","journal-title":"Environmetrics"},{"key":"423_CR20","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s00477-012-0559-z","volume":"26","author":"M.D. Ruiz-Medina","year":"2012","unstructured":"Ruiz-Medina, M.D., Espejo, R.M.: Spatial autoregressive functional plug-in prediction of ocean surface temperature. Stoch. Environ. Res. Risk Assess. 26, 335\u2013344 (2012)","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"423_CR21","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.jag.2012.01.021","volume":"22","author":"M.D. Ruiz-Medina","year":"2013","unstructured":"Ruiz-Medina, M.D., Espejo, R.M.: Integration of spatial functional interaction in the extrapolation of ocean surface temperature anomalies due to global warming. Int. J. Appl. Earth Obs. Geoinf. 22, 27\u201339 (2013)","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"423_CR22","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s00477-009-0306-2","volume":"24","author":"M.D. Ruiz-Medina","year":"2010","unstructured":"Ruiz-Medina, M.D., Salmer\u00f3n, R.: Functional maximum-likelihood estimation of ARH(p) models. Stoch. Environ. Res. Risk Assess. 24, 131\u2013146 (2010)","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"423_CR23","doi-asserted-by":"crossref","DOI":"10.1142\/5970","volume-title":"Random Fields Estimation","author":"A.G. Ramm","year":"2005","unstructured":"Ramm, A.G.: Random Fields Estimation. World Scientific, New York (2005)"},{"key":"423_CR24","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s00477-009-0343-x","volume":"24","author":"M.D. Ruiz-Medina","year":"2010","unstructured":"Ruiz-Medina, M.D., Fern\u00e1ndez-Pascual, R.: Spatiotemporal filtering from fractal spatial functional data sequences. Stoch. Environ. Res. Risk Assess. 24, 527\u2013538 (2010)","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"423_CR25","first-page":"19","volume":"31","author":"K. Kikuchi","year":"1995","unstructured":"Kikuchi, K., Negoro, A.: Pseudo differential operators with variable order of differentiation. Natural Sci. 31, 19\u201327 (1995). Reports of the Faculty of Liberal Arts, Shizuoka University","journal-title":"Natural Sci."},{"key":"423_CR26","doi-asserted-by":"crossref","first-page":"69","DOI":"10.4171\/ZAA\/337","volume":"8","author":"H.-G. Leopold","year":"1989","unstructured":"Leopold, H.-G.: On Besov spaces of variable order of differentiation. Z. Anal. Anwend. 8, 69\u201382 (1989)","journal-title":"Z. Anal. Anwend."},{"key":"423_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/form.1991.3.1","volume":"3","author":"H.-G. Leopold","year":"1991","unstructured":"Leopold, H.-G.: On function spaces of variable order of differentiation. Forum Math. 3, 1\u201321 (1991)","journal-title":"Forum Math."},{"key":"423_CR28","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1023\/A:1022483721944","volume":"49","author":"H.-G. Leopold","year":"1999","unstructured":"Leopold, H.-G.: Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration. Czechoslov. Math. J. 49, 633\u2013644 (1999)","journal-title":"Czechoslov. Math. J."},{"key":"423_CR29","volume-title":"The Geometry of Random Fields","author":"R.J. Adler","year":"1981","unstructured":"Adler, R.J.: The Geometry of Random Fields. Wiley, Chichester (1981)"},{"key":"423_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-3873-1","volume-title":"Probability Distributions in Banach Spaces","author":"N.N. Vakhania","year":"1987","unstructured":"Vakhania, N.N., Tarieladze, V.I., Chebonyan, S.A.: Probability Distributions in Banach Spaces. Reidel, Dordrecht (1987)"},{"key":"423_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-66282-9","volume-title":"Perturbation Theory of Linear Operators","author":"T. Kato","year":"1995","unstructured":"Kato, T.: Perturbation Theory of Linear Operators. Springer, Berlin (1995)"},{"key":"423_CR32","volume-title":"Linear Operators. Part II: Spectral Theory","author":"N. Dunford","year":"1963","unstructured":"Dunford, N., Schwartz, J.T.: Linear Operators. Part II: Spectral Theory. Interscience, New York (1963)"},{"key":"423_CR33","volume-title":"Interpolation Theory, Function Spaces, Differential Operators","author":"H. Triebel","year":"1978","unstructured":"Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam (1978)"},{"key":"423_CR34","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/S0378-3758(98)00244-4","volume":"80","author":"V.V. Anh","year":"1999","unstructured":"Anh, V.V., Angulo, J.M., Ruiz-Medina, M.D.: Possible long-range dependence in fractional random fields. J. Stat. Plan. Inference 80, 95\u2013110 (1999)","journal-title":"J. Stat. Plan. Inference"},{"key":"423_CR35","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1239\/aap\/1231340167","volume":"40","author":"V. Anh","year":"2008","unstructured":"Anh, V., Leonenko, N.N., Shieh, N.-R.: Multifractality of products of geometric Ornstein\u2013Uhlenbeck-type processes. Adv. Appl. Probab. 40, 1129\u20131156 (2008)","journal-title":"Adv. Appl. Probab."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0423-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-013-0423-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0423-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T17:27:56Z","timestamp":1563989276000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-013-0423-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,24]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["423"],"URL":"https:\/\/doi.org\/10.1007\/s10957-013-0423-4","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,24]]}}}