Marginal longitudinal semiparametric regression via penalized splines

Abstract

We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.

Pemodelan Regresi Nonparametrik Menggunakan Pendekatan Polinomial Lokal Pada Beban Listrik Di Kota Semarang

“…Pada prosedur regresi nonparamterik, data akan mencari sendiri bentuk kurva regresinya tanpa dipengaruhi oleh subjektivitas peneliti. Beberapa model regresi nonparametrik yang telah dikembangkan antara lain Penalized Spline (Kadiri et al, 2010), Smoothing Spline (Eubank et al, 2004), Regresi Spline Multirespon (Lestari et al, 2010), Regresi Menggunakan Kernel (Hu et al, 2004), Kernel of Smoothing Spline (Lin et al, 2004) dan Polinomial Lokal (Wu dan Zhang, 2006) Polinomial lokal mempunyai beberapa kelebihan antara lain dapat mengurangi asimtotik bias dan menghasilkan estimasi yang baik (Welsh dan Yee, 2005). Estimasi Polinomial Lokal dapat menggunakan WLS (Weighted Least Square) dengan cara meminimumkannya (Takezawa, 2006).…”

Linear Penalized Spline Model Estimation Using Ranked Set Sampling Technique

“…[3] studied asymptotic properties of the penalized estimators. [1] introduced penalized spline models to marginal models with application to longitudinal data.…”

“…Particularly, he selected m simple random subsamples each of size m from the target population, say {x 1 , x 2 , ..., x m } 1 ; {x 1 , x 2 , ..., x m } 2 ; ...; {x 1 , x 2 , ..., x m } m . Then he ordered each subsample separately to produce ranked subsets {x (1) …”

“…Ordering can be performed by any relatively cheap method. Then from the first subsample, choose the first minimum-response value linked with the correspondence predictor value; which can be denoted by (x [1] , y (1) ) 1 , from the second subsample choose the second minimum-response pair (x [2] , y (2) ) 2 and finally, from the last subsample choose the maximum-response pair (x [3] , y (3) ) 3 . Generally in this research, the pair (x [i] , y (i) ) j means that i th predictor value x [i] corresponds to the i th minimum-response value y (i) from the j th subsample.…”

“…Generally in this research, the pair (x [i] , y (i) ) j means that i th predictor value x [i] corresponds to the i th minimum-response value y (i) from the j th subsample. So, the yielded RSS set of size 3 is {(x [1] , y (1) ) 1 , (x [2] , y (2) ) 2 , (x [3] , y (3) ) 3 } which can be used to estimate the regression model.…”