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Obtaining a closed-form expression for the likelihood function to apply the maximum likelihood estimation method is a difficult, sometimes impossible, task. We compared the known Laplace approximation method with the delta method to approximate the integrals involved in the likelihood function. These approaches were adapted to allow the estimation of the parameters even when the requirement of most existing methods, namely having the same age vector of observations for all trajectories, fails, as it did in our real data example. Simulation studies were also performed to assess the performance of these approximation methods. The results show that the approximation methods under study are a very good alternative for the estimation of SDE mixed models.<\/p><\/abstract><\/jats:p>","DOI":"10.3934\/math.2024383","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T12:36:40Z","timestamp":1708951000000},"page":"7866-7894","source":"Crossref","is-referenced-by-count":2,"title":["Estimation for stochastic differential equation mixed models using approximation methods"],"prefix":"10.3934","volume":"9","author":[{"given":"Nelson T.","family":"Jamba","sequence":"first","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es, Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora, \u00c9vora, Portugal"},{"name":"Liceu n\u00ba 918 do munic\u00edpio dos Gambos, Chiange, Gambos, Angola and Instituto Superior de Ci\u00eancias de Educa\u00e7\u00e3o da Hu\u00edla, Lubango, Hu\u00edla, Angola"}]},{"given":"Gon\u00e7alo","family":"Jacinto","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es, Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora, \u00c9vora, Portugal"},{"name":"Departamento de Matem\u00e1tica, Escola de Ci\u00eancia e Tecnologia, Universidade de \u00c9vora, \u00c9vora, Portugal"}]},{"given":"Patr\u00edcia A.","family":"Filipe","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es, Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora, \u00c9vora, Portugal"},{"name":"Departamento de M\u00e9todos Quantitativos para Gest\u00e3o e Economia, ISCTE Business School, Iscte-Instituto Universit\u00e1rio de Lisboa, Lisboa, Portugal"}]},{"given":"Carlos A.","family":"Braumann","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es, Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora, \u00c9vora, Portugal"},{"name":"Departamento de Matem\u00e1tica, Escola de Ci\u00eancia e Tecnologia, Universidade de \u00c9vora, \u00c9vora, Portugal"}]}],"member":"2321","reference":[{"key":"key-10.3934\/math.2024383-1","unstructured":"P. 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