{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:22:41Z","timestamp":1760232161644,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T00:00:00Z","timestamp":1666051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001321","name":"National Research Foundation (NRF) of South Africa","doi-asserted-by":"publisher","award":["71199","114613"],"award-info":[{"award-number":["71199","114613"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]},{"name":"South African DST-NRF-MRC SARChI Research Chair in Biostatistics","award":["71199","114613"],"award-info":[{"award-number":["71199","114613"]}]},{"name":"STATOMET at the Department of Statistics at the University of Pretoria and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa","award":["71199","114613"],"award-info":[{"award-number":["71199","114613"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Additional information and borrowing strength from the related sites and other sources will improve estimation in small areas. Generalized linear mixed-effects models (GLMMs) have been frequently used in small area estimation; however, the relationship between the response variable and some covariates may not be linear in many cases. In such cases, using semiparametric modeling, incorporating some nonlinear symmetric\/asymmetric functions to the predictor seems more appropriate due to their flexibility. In addition, spatial dependence is observed between areas in many cases. Thus, using the semiparametric spatial models for small areas is of interest. This paper presents semiparametric spatial GLMMs and approximates the nonlinear component using splines to estimate the linear part. We apply our proposal for analyzing insurance data obtained from an Iranian insurance company. Our numerical illustrations will support the use of our proposal in situations where the spatial GLMMs may not be appropriate.<\/jats:p>","DOI":"10.3390\/sym14102194","type":"journal-article","created":{"date-parts":[[2022,10,19]],"date-time":"2022-10-19T02:54:25Z","timestamp":1666148065000},"page":"2194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Small Area Estimation Using a Semiparametric Spatial Model with Application in Insurance"],"prefix":"10.3390","volume":"14","author":[{"given":"Seyede Elahe","family":"Hosseini","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davood","family":"Shahsavani","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Reza","family":"Rabiei","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5881-9241","authenticated-orcid":false,"given":"Mohammad","family":"Arashi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran"},{"name":"Department of Statistics, University of Pretoria, Pretoria 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hossein","family":"Baghishani","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood 3619995161, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,18]]},"reference":[{"key":"ref_1","first-page":"19","article-title":"Small area estimation of poverty indicators under partitioned area-level time models","volume":"39","author":"Morales","year":"2015","journal-title":"SORT"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1007\/s11749-015-0469-8","article-title":"Empirical best prediction under area-level Poisson mixed models","volume":"25","author":"Boubeta","year":"2016","journal-title":"Test"},{"key":"ref_3","first-page":"223","article-title":"A Bayesian semi-parametric model for small area estimation","volume":"3","author":"Malec","year":"2008","journal-title":"IMS Collect."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1080\/03610926.2017.1317806","article-title":"Small area estimation of proportions under a spatial dependent aggregated level random effects model","volume":"47","author":"Chandra","year":"2018","journal-title":"Commun. 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