scholarly journals Nonparametric estimation of an additive model with a link function

2004 ◽  
Vol 32 (6) ◽  
pp. 2412-2443 ◽  
Author(s):  
Joel L. Horowitz ◽  
Enno Mammen
Keyword(s):  
Nonparametric Estimation ◽  
Additive Model ◽  
Link Function

ORACLE-EFFICIENT NONPARAMETRIC ESTIMATION OF AN ADDITIVE MODEL WITH AN UNKNOWN LINK FUNCTION

2010 ◽  
Vol 27 (3) ◽  
pp. 582-608 ◽  
Author(s):  
Joel L. Horowitz ◽  
Enno Mammen
Keyword(s):  
Nonparametric Estimation ◽  
Finite Dimension ◽  
Explanatory Variable ◽  
Additive Model ◽  
The Other ◽  
Convergence In Probability ◽  
Link Function ◽  
Additive Component ◽  
Second Derivatives ◽  
Unknown Link

This paper describes an estimator of the additive components of a nonparametric additive model with an unknown link function. When the additive components and link function are twice differentiable with sufficiently smooth second derivatives, the estimator is asymptotically normally distributed with a rate of convergence in probability ofn−2/5. This is true regardless of the (finite) dimension of the explanatory variable. Thus, the estimator has no curse of dimensionality. Moreover, the asymptotic distribution of the estimator of each additive component is the same as it would be if the link function and the other components were known with certainty. Thus, asymptotically there is no penalty for not knowing the link function or the other components.

Perbandingan Linieritas Dalam Pendeteksian Faktor-Faktor Yang Mempengaruhi Angka Kematian Bayi Di Provinsi Aceh

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Desfira Ahya ◽  
Inas Salsabila ◽  
Miftahuddin
Keyword(s):  
Mortality Rate ◽  
Infant Mortality ◽  
Linear Model ◽  
Health Workers ◽  
Additive Model ◽  
Infant Mortality Rate ◽  
Mortality Data ◽  
Important Indicator ◽  
Penalized Spline ◽  
Aceh Province

Angka Kematian Bayi/ Infant Mortality Rate (IMR) merupakan indikator penting dalam mengukur keberhasilan pengembangan kesehatan. Nilai IMR juga dapat digunakan untuk mengetahui tingkat kesehatan ibu, kondisi kesehatan lingkungan dan secara umum, tingkat pengembangan sosio-ekonomi masyarakat. Penelitian ini bertujuan untuk memperoleh model IMR terbaik menggunakan tiga pendekatan: Model Linear, Model Linear Tergeneralisir dan Model Aditif Tergeneralisir dengan basis P-spline. Sebagai tambahan, berdasarkan model tersebut akan terlihat variabel yang mempengaruhi tingkat kematian bayi di provinsi Aceh. Penelitian ini menggunakan data jumlah kematian bayi di tahun 2013-2015. Data dalam penelitian ini diperoleh dari Profil Kesehatan Aceh. Hasil menunjukkan bahwa model terbaik dalam menjelaskan angka kematian bayi di provinsi Aceh tahun 2013-2015 ialah Model Linear Tergeneralisir dengan basis P-spline menggunakan parameter penghalusan 100 dan titik knots 8. Faktor yang sangat mempengaruhi angka kematian ialah jumlah pekerja yang sehat.   Infant mortality rate (IMR) is an important indicator in measuring the success of health development. IMR also can be used to knowing the level of maternal health, environmental health conditions and generally the level of socio-economic development in community. This research aims to get the best model of infant mortality data using three approaches: Linear Model, Generalized Linear Model and Generalized Additive Model with Penalized Spline (P-spline) base. In addition, based on the model can be seen the variables that affect to infant mortality in Aceh Province. This research uses data number of infant mortality in Aceh Province period 2013-2015. The data in this research were obtained from Aceh’s Health Profile. The results show that the best model can be explain infant mortality rate in Aceh Province period 2013-2015 is GAM model with P-spline base using smoothing parameter 100 and knots 8. Factor that high effect to infant mortality is number of health workers.

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