Hosseini, Seyede ElaheShahsavani, DavoodRabiei, Mohammad RezaArashi, MohammadBaghishani, Hossein2023-03-062023-03-062022-10-18Hosseini, S.E.; Shahsavani, D.; Rabiei, M.R.; Arashi, M.; Baghishani, H. Small Area Estimation Using a Semiparametric Spatial Model with Application in Insurance. Symmetry 2022, 14, 2194. https://DOI.org/10.3390/sym14102194.2073-8994 (online)10.3390/sym14102194https://repository.up.ac.za/handle/2263/89960Additional 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.en© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Insurance dataSemiparametric modelSmall areaSpatial analysisSplineGeneralized linear mixed-effects model (GLMM)Article