{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T15:39:19Z","timestamp":1759937959795,"version":"3.33.0"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2008,3,19]],"date-time":"2008-03-19T00:00:00Z","timestamp":1205884800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2008,9]]},"DOI":"10.1007\/s11222-008-9057-z","type":"journal-article","created":{"date-parts":[[2008,3,18]],"date-time":"2008-03-18T18:30:27Z","timestamp":1205865027000},"page":"297-312","source":"Crossref","is-referenced-by-count":17,"title":["SiZer Map for inference with additive models"],"prefix":"10.1007","volume":"18","author":[{"given":"W.","family":"Gonz\u00e1lez-Manteiga","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. D.","family":"Mart\u00ednez-Miranda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Raya-Miranda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,3,19]]},"reference":[{"key":"9057_CR1","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1111\/j.2517-6161.1993.tb01923.x","volume":"55","author":"A. Azzalini","year":"1993","unstructured":"Azzalini, A., Bowman, A.W.: On the use of nonparametric regression for checking linear relationships. J. R. Stat. Soc. Ser. B 55, 549\u2013557 (1993)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"9057_CR2","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1214\/aos\/1176349024","volume":"21","author":"D. Barry","year":"1993","unstructured":"Barry, D.: Testing for additivity of a regression function. Ann. Stat. 21, 235\u2013254 (1993)","journal-title":"Ann. Stat."},{"key":"9057_CR3","volume-title":"Empirical Model-Building and Response Surfaces","author":"G.E.P. Box","year":"1987","unstructured":"Box, G.E.P., Draper, N.: Empirical Model-Building and Response Surfaces. Wiley, New York (1987)"},{"key":"9057_CR4","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1080\/01621459.1985.10478157","volume":"80","author":"L. Breiman","year":"1985","unstructured":"Breiman, L., Friedman, J.H.: Estimating optimal transformations for multiple regression and correlation. J. Am. Stat. Assoc. 80, 580\u2013598 (1985)","journal-title":"J. Am. Stat. Assoc."},{"issue":"447","key":"9057_CR5","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1080\/01621459.1999.10474186","volume":"94","author":"P. Chaudhuri","year":"1999","unstructured":"Chaudhuri, P., Marron, J.S.: SiZer for exploration of structures in curves. J. Am. Stat. Assoc. 94(447), 807\u2013823 (1999)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR6","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1214\/aos\/1016218224","volume":"28","author":"P. Chaudhuri","year":"2000","unstructured":"Chaudhuri, P., Marron, J.S.: Scale space view of curve estimation. Ann. Stat. 28, 408\u2013428 (2000)","journal-title":"Ann. Stat."},{"key":"9057_CR7","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1080\/01621459.1988.10478639","volume":"83","author":"W. Cleveland","year":"1988","unstructured":"Cleveland, W., Devlin, S.: Locally weighted regression: an approach to regression analysis by local fitting. J. Am. Stat. Assoc. 83, 596\u2013610 (1988)","journal-title":"J. Am. Stat. Assoc."},{"issue":"438","key":"9057_CR8","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1080\/01621459.1997.10474002","volume":"92","author":"R.D. Cook","year":"1997","unstructured":"Cook, R.D., Weisberg, S.: Graphics for assessing the adequacy of regression models. J. Am. Stat. Assoc. 92(438), 490\u2013499 (1997)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR9","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316948","volume-title":"Applied Regression Including Computing and Graphics","author":"R.D. Cook","year":"1999","unstructured":"Cook, R.D., Weisberg, S.: Applied Regression Including Computing and Graphics. Wiley, New York (1999a)"},{"issue":"1","key":"9057_CR10","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1080\/00031305.1999.10474426","volume":"53","author":"R.D. Cook","year":"1999","unstructured":"Cook, R.D., Weisberg, S.: Graphs in statistical analysis: is the medium the message? Am. Stat. 53(1), 29\u201337 (1999b)","journal-title":"Am. Stat."},{"key":"9057_CR11","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1023\/A:1016113704805","volume":"54","author":"S. Derbort","year":"2002","unstructured":"Derbort, S., Dette, H., Munk, A.: A test for additivity in nonparametric regression. Ann. Inst. Stat. Math. 54, 60\u201382 (2002)","journal-title":"Ann. Inst. Stat. Math."},{"key":"9057_CR12","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1006\/jmva.2000.1913","volume":"76","author":"H. Dette","year":"2001","unstructured":"Dette, H., Derbort, S.: Analysis of variance in nonparametric regression models. J. Multivar. Anal. 76, 110\u2013137 (2001)","journal-title":"J. Multivar. Anal."},{"key":"9057_CR13","doi-asserted-by":"crossref","first-page":"669","DOI":"10.2307\/3318732","volume":"7","author":"H. Dette","year":"2001","unstructured":"Dette, H., von Lieres und Wilkau, C.: Testing additivity by kernel-based methods\u2014what is a reasonable test? Bernoulli 7, 669\u2013697 (2001)","journal-title":"Bernoulli"},{"key":"9057_CR14","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1080\/10485250410001713972","volume":"17","author":"H. Dette","year":"2005","unstructured":"Dette, H., von Lieres und Wilkau, C., Sperlich, S.: A comparison of different nonparametric methods for inference on additive models. J. Nonparametr. Stat. 17, 57\u201381 (2005)","journal-title":"J. Nonparametr. Stat."},{"key":"9057_CR15","doi-asserted-by":"crossref","first-page":"1896","DOI":"10.1214\/aos\/1034713639","volume":"23","author":"R.L. Eubank","year":"1995","unstructured":"Eubank, R.L., Hart, J.D., Simpson, D.G., Stefanski, L.A.: Testing for additivity in nonparametric regression. Ann. Stat. 23, 1896\u20131920 (1995)","journal-title":"Ann. Stat."},{"issue":"471","key":"9057_CR16","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1198\/016214504000001439","volume":"100","author":"J. Fan","year":"2005","unstructured":"Fan, J., Jiang, J.: Nonparametric inferences for additive models. J. Am. Stat. Assoc. 100(471), 890\u2013907 (2005)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR17","first-page":"280","volume":"34","author":"N.L. Franklin","year":"1956","unstructured":"Franklin, N.L., Pinchbeck, P.H., Popper, F.: A statistical approach to catalyst development, part\u00a0I: the effect of process variables in the vapor phase oxidation of naphthalene. Trans. Inst. Chem. Eng. 34, 280\u2013293 (1956)","journal-title":"Trans. Inst. Chem. Eng."},{"key":"9057_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1198\/106186002317375596","volume":"11","author":"F. Godtliebsen","year":"2002","unstructured":"Godtliebsen, F., Marron, J.S., Chaudhuri, P.: Significance in scale space for bivariate density estimation. J. Comput. Graph. Stat. 11, 1\u201321 (2002)","journal-title":"J. Comput. Graph. Stat."},{"key":"9057_CR19","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF02562674","volume":"2","author":"W. Gonz\u00e1lez-Manteiga","year":"1993","unstructured":"Gonz\u00e1lez-Manteiga, W., Cao, R.: Testing hypothesis of general linear model using nonparametric regression estimation. Test 2, 161\u2013189 (1993)","journal-title":"Test"},{"key":"9057_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0304-4076(01)00049-5","volume":"104","author":"P.L. Gozalo","year":"2001","unstructured":"Gozalo, P.L., Linton, O.B.: Testing additivity in generalized nonparametric regression with estimated parameters. J. Econom. 104, 1\u201348 (2001)","journal-title":"J. Econom."},{"key":"9057_CR21","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1080\/01621459.1992.10476260","volume":"87","author":"C. Gu","year":"1992","unstructured":"Gu, C.: Diagnostics for nonparametric regression models with additive terms. J. Am. Stat. Assoc. 87, 1051\u20131058 (1992)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR22","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1080\/01621459.2000.10474271","volume":"95","author":"P. Gustafson","year":"2000","unstructured":"Gustafson, P.: Bayessian regression modelling with interactions and smooth effects. J. Am. Stat. Assoc. 95, 795\u2013806 (2000)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR23","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1198\/016214505000001294","volume":"101","author":"J. Hannig","year":"2006","unstructured":"Hannig, J., Marron, J.S.: Advanced distribution theory for SiZer. J. Am. Stat. Assoc. 101, 484\u2013499 (2006)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR24","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1017\/S026646660420202X","volume":"20","author":"W. H\u00e4rdle","year":"2004","unstructured":"H\u00e4rdle, W., Huet, S., Mammen, E., Sperlich, S.: Bootstrap inference in semiparametric generalized additive models. Econom. Theory 20, 265\u2013300 (2004)","journal-title":"Econom. Theory"},{"issue":"4","key":"9057_CR25","doi-asserted-by":"crossref","first-page":"1926","DOI":"10.1214\/aos\/1176349403","volume":"21","author":"W. H\u00e4rdle","year":"1993","unstructured":"H\u00e4rdle, W., Mammen, E.: Comparing nonparametric versus parametric regression fits. Ann. Stat. 21(4), 1926\u20131947 (1993)","journal-title":"Ann. Stat."},{"key":"9057_CR26","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1198\/016214501753382264","volume":"96","author":"W. H\u00e4rdle","year":"2001","unstructured":"H\u00e4rdle, W., Sperlich, S., Spokoiny, V.: Structural tests in additive regression. J. Am. Stat. Assoc. 96, 1333\u20131347 (2001)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR27","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1080\/01621459.1987.10478440","volume":"82","author":"T.J. Hastie","year":"1987","unstructured":"Hastie, T.J., Tibshirani, R.: Generalized additive models: some applications. J. Am. Stat. Assoc. 82, 371\u2013386 (1987)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR28","volume-title":"Generalized Additive Models","author":"T.J. Hastie","year":"1990","unstructured":"Hastie, T.J., Tibshirani, R.: Generalized Additive Models. Chapman & Hall, New York (1990)"},{"key":"9057_CR29","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1111\/1468-0262.00207","volume":"69","author":"J.L. Horowitz","year":"2001","unstructured":"Horowitz, J.L., Spokoiny, V.G.: An adaptative, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599\u2013631 (2001)","journal-title":"Econometrica"},{"key":"9057_CR30","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/10485250500334366","volume":"18","author":"C.S. Kim","year":"2006","unstructured":"Kim, C.S., Marron, J.S.: SiZer for jump detection. J. Nonparametr. Stat. 18, 13\u201320 (2006)","journal-title":"J. Nonparametr. Stat."},{"key":"9057_CR31","first-page":"476","volume":"67","author":"R. Li","year":"2005","unstructured":"Li, R., Marron, J.S.: Local likelihood SiZer Map. Sankhya Indian J. Stat. 67, 476\u2013498 (2005)","journal-title":"Sankhya Indian J. Stat."},{"key":"9057_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-6465-9","volume-title":"Scale Space Theory in Computer Vision","author":"T. Lindeberg","year":"1994","unstructured":"Lindeberg, T.: Scale Space Theory in Computer Vision. Kluwer Academic, Dordrecht (1994)"},{"key":"9057_CR33","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0378-3758(02)00506-2","volume":"121","author":"J.S. Marron","year":"2004","unstructured":"Marron, J.S., de U\u00f1a \u00c1lvarez, J.: SiZer for length biased, censored density and hazard estimation. J. Stat. Plan. Inference 121, 149\u2013161 (2004)","journal-title":"J. Stat. Plan. Inference"},{"key":"9057_CR34","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1023\/A:1008890315909","volume":"9","author":"J.S. Marron","year":"1999","unstructured":"Marron, J.S., Udina, F.: Interactive local bandwidth choice. Stat. Comput. 9, 101\u2013110 (1999)","journal-title":"Stat. Comput."},{"key":"9057_CR35","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/BF02741310","volume":"20","author":"J.S. Marron","year":"2005","unstructured":"Marron, J.S., Zhang, J.T.: SiZer for smoothing splines. Comput. Stat. 20, 481\u2013502 (2005)","journal-title":"Comput. Stat."},{"key":"9057_CR36","doi-asserted-by":"crossref","unstructured":"Opsomer, J.D., Francisco-Fern\u00e1ndez, M.: Finding local departures from a parametric model using nonparametric regression. Stat. Pap. (Published online: 9 January 2008)","DOI":"10.1007\/s00362-007-0116-x"},{"key":"9057_CR37","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1214\/aos\/1034276626","volume":"25","author":"J.D. Opsomer","year":"1997","unstructured":"Opsomer, J.D., Ruppert, D.: Fitting a bivariate additive model by local polynomial regression. Ann. Stat. 25, 186\u2013211 (1997)","journal-title":"Ann. Stat."},{"key":"9057_CR38","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1080\/01621459.1998.10473714","volume":"93","author":"J.D. Opsomer","year":"1998","unstructured":"Opsomer, J.D., Ruppert, D.: A fully automated bandwidth selection method for fitting additive models. J. Am. Stat. Assoc. 93, 605\u2013619 (1998)","journal-title":"J. Am. Stat. Assoc."},{"key":"9057_CR39","unstructured":"Park, C., Kang, K.: SiZer analysis for the comparison of regression curves. Unpublished manuscript (2007)"},{"issue":"8","key":"9057_CR40","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1080\/0266476042000270554","volume":"31","author":"C. Park","year":"2004","unstructured":"Park, C., Marron, J.S., Rondonotti, V.: Dependent SiZer: goodness-of-fit tests for time series models. J. Appl. Stat. 31(8), 999\u20131017 (2004)","journal-title":"J. Appl. Stat."},{"key":"9057_CR41","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s11222-005-4072-9","volume":"15","author":"J. Roca-Pardi\u00f1as","year":"2005","unstructured":"Roca-Pardi\u00f1as, J., Cadarso-Su\u00e1rez, C., Gonz\u00e1lez-Manteiga, W.: Testing for interactions in generalized additive models: application to SO2 pollution data. Stat. Comput. 15, 289\u2013299 (2005)","journal-title":"Stat. Comput."},{"key":"9057_CR42","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1214\/07-EJS006","volume":"1","author":"V. Rondonotti","year":"2007","unstructured":"Rondonotti, V., Marron, J.S., Park, C.: SiZer for time series: a new approach to the analysis of trends. Electron. J. Stat. 1, 268\u2013289 (2007)","journal-title":"Electron. J. Stat."},{"key":"9057_CR43","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511755453","volume-title":"Semiparametric Regression","author":"D. Ruppert","year":"2003","unstructured":"Ruppert, D., Wand, M.P., Carroll, R.J.: Semiparametric Regression. Cambridge University Press, Cambridge (2003)"},{"key":"9057_CR44","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1017\/S0266466602182016","volume":"18","author":"S. Sperlich","year":"2002","unstructured":"Sperlich, S., Tj\u00f8stheim, D., Yang, L.: Nonparametric estimation and testing of interaction in additive models. Econom. Theory 18, 197\u2013251 (2002)","journal-title":"Econom. Theory"},{"key":"9057_CR45","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1214\/aos\/1176349548","volume":"13","author":"C.J. Stone","year":"1985","unstructured":"Stone, C.J.: Additive regression and other nonparametric models. Ann. Stat. 13, 689\u2013705 (1985)","journal-title":"Ann. Stat."},{"key":"9057_CR46","doi-asserted-by":"crossref","first-page":"232","DOI":"10.2307\/3001938","volume":"5","author":"J. Tukey","year":"1949","unstructured":"Tukey, J.: On degree of freedom test for non-additivity. Biometrics 5, 232\u2013242 (1949)","journal-title":"Biometrics"},{"key":"9057_CR47","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/S0378-3758(02)00163-5","volume":"115","author":"L. Yang","year":"2003","unstructured":"Yang, L., Sperlich, W., H\u00e4rdle, W.: Derivative estimation and testing in generalized additive models. J. Stat. Plan. Inference 115, 521\u2013542 (2003)","journal-title":"J. Stat. Plan. Inference"},{"key":"9057_CR48","doi-asserted-by":"crossref","first-page":"151","DOI":"10.2307\/3316065","volume":"31","author":"C.M. Zhang","year":"2003","unstructured":"Zhang, C.M.: Adaptative tests of regression functions via multiscale generalized likelihood ratios. Can. J. Stat. 31, 151\u2013171 (2003)","journal-title":"Can. J. Stat."},{"key":"9057_CR49","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/0304-4076(95)01760-7","volume":"75","author":"J.X. Zheng","year":"1996","unstructured":"Zheng, J.X.: A consistent test of a functional form via nonparametric estimation techniques. J. Econom. 75, 263\u2013289 (1996)","journal-title":"J. Econom."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-008-9057-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-008-9057-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-008-9057-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T04:27:29Z","timestamp":1738124849000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-008-9057-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3,19]]},"references-count":49,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["9057"],"URL":"https:\/\/doi.org\/10.1007\/s11222-008-9057-z","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2008,3,19]]}}}