Abstract:
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.
