Non-Parametric Small Area Estimation Using Penalized Spline Regression

Abstract

The paper proposes a small area estimation approach that combines small area random effects with a smooth, non-parametrically specified trend. By using penalized splines as the representation for the non-parametric trend, it is possible to express the non-parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean-squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non-parametric bootstrap approach for model inference and estimation of the small area prediction mean-squared error. The applicability of the method is demonstrated on a survey of lakes in north-eastern USA. Copyright 2008 Royal Statistical Society.

Spatio‐temporal modeling of mortality risks using penalized splines

“…Das et al (2004) show that the approximation is also valid when the variance components are estimated by ML and REML. Singh et al (2005) extend the Prasad-Rao MSE estimator for spatio-temporal models, and very recently, Opsomer et al (2008) justify the approximation in the P-spline context. These authors propose the following estimator for the MSE…”

Pemetaan Kemiskinan di Kabupaten Mukomuko Menggunakan Small Area Estimation Dengan Pendekatan Regresi Penalized Spline

“…Opsomer (2008) menggunakan P-Spline untuk mengestimasi area kecil dengan menambahkan pengaruh acak area kecil pada persamaan (7), sehingga diperoleh [8]: e = + Y Xβ + Zγ + Du Penduga terbaik untuk variabel prediktor γ dan u diperoleh dengan meminimumkan MSE dari γ dan u . Sehingga diperoleh prediktor linier tak bias terbaik (BLUP) untuk γ dan u sebagai berikut: …”

“…Sehingga pendekatan nonparametrik menjadi alternatif pilihan. Salah satu pendekatan nonparametrik yang digunakan adalah Regresi Penalized Spline (P-Spline) [8].…”

“…Berbagai penelitian yang berkaitan dengan small area estimation dengan pendekatan nonparametrik telah banyak dilakukan antara lain Baskara (2014) [8].…”

Estimating small area proportions with kernel logistic regressions models

“…The linear mixed effects model is useful for estimating the small area means efficiently under normality assumptions. Nonlinear SAE can be found in Opsomer et al (2008), Salvati et al (2011), Shim and Hwang (2012) and . In this paper, we consider the situation when the estimate to be produced is proportion at small area level.…”