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This is first illustrated when interested in the temporal trend of a single neuron. An approach to investigate the maximal firing rate, based on the penalizedspline model is proposed. Determination of the time of maximal firing rate is based on non\u2010linear optimization of the objective function with the corresponding confidence intervals constructed based on the first\u2010order derivative function. To distinguish between the curves from different experimental conditions in a moment\u2010by\u2010moment sense, bias adjusted simulation\u2010based simultaneous confidence bands leading to global inference in the time domain are constructed. The bands are an extension of the approach proposed by Ruppert et al. (2003). These methods are in a second step extended towards the analysis of a population of neurons via a marginal or population\u2010averaged model (\u00a9 2009 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/bimj.200810501","type":"journal-article","created":{"date-parts":[[2009,2,7]],"date-time":"2009-02-07T02:48:46Z","timestamp":1233974926000},"page":"203-216","source":"Crossref","is-referenced-by-count":2,"title":["Application of Penalized Splines in Analyzing Neuronal Data"],"prefix":"10.1002","volume":"51","author":[{"given":"John T.","family":"Maringwa","sequence":"first","affiliation":[]},{"given":"Christel","family":"Faes","sequence":"additional","affiliation":[]},{"given":"Helena","family":"Geys","sequence":"additional","affiliation":[]},{"given":"Geert","family":"Molenberghs","sequence":"additional","affiliation":[]},{"given":"Carmen","family":"Cadarso\u2010Su\u00e1rez","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9 L.","family":"Pardo\u2010V\u00e1zquez","sequence":"additional","affiliation":[]},{"given":"V\u00edctor","family":"Lebor\u00e1n","sequence":"additional","affiliation":[]},{"given":"Carlos","family":"Acun\u00f1a","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,2,13]]},"reference":[{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2195"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.2.419"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01890836"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9876.2006.00545.x"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1999.10474186"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.1.91"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/88.4.1055"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1991"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1038425655"},{"key":"e_1_2_1_11_1","doi-asserted-by":"crossref","unstructured":"Efron B.andTibshirani R. 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