title: Functional Mixed Effects Model for Small Area Estimation.
abstract: Functional data analysis has become an important area of research due to its ability of handling high dimensional and complex data structures. However, the development is limited in the context of linear mixed effect models, and in particular, for small area estimation. The linear mixed effect models are the backbone of small area estimation. In this article, we consider area level data, and fit a varying coefficient linear mixed effect model where the varying coefficients are semi-parametrically modeled via B-splines. We propose a method of estimating the fixed effect parameters and consider prediction of random effects that can be implemented using a standard software. For measuring prediction uncertainties, we derive an analytical expression for the mean squared errors, and propose a method of estimating the mean squared errors. The procedure is illustrated via a real data example, and operating characteristics of the method are judged using finite sample simulation studies.
authors: Department of Statistics & Probability, Michigan State University, East Lansing, MI 48824.
authors: Tapabrata
authors: T
authors: Maiti
authors: Department of Statistics, Texas A&M University, College Station, TX 77843.
authors: Samiran
authors: S
authors: Sinha
authors: Department of Statistics & Probability, Michigan State University, East Lansing, MI 48824.
authors: Ping-Shou
authors: PS
authors: Zhong
keywords: B-splines; Best linear unbiased predictor; Functional data analysis; Linear mixed models; Mean squared error; Restricted maximum likelihood; Small area estimation; Variance components