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Polynomial Spline Estimation for a Generalized Additive Coefficient Model
Author(s) -
XUE LAN,
LIANG HUA
Publication year - 2010
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2009.00655.x
Subject(s) - mathematics , spline (mechanical) , polynomial , smoothing spline , estimation , statistics , mathematical analysis , spline interpolation , engineering , management , economics , bilinear interpolation , structural engineering
. We study a semiparametric generalized additive coefficient model (GACM), in which linear predictors in the conventional generalized linear models are generalized to unknown functions depending on certain covariates, and approximate the non‐parametric functions by using polynomial spline. The asymptotic expansion with optimal rates of convergence for the estimators of the non‐parametric part is established. Semiparametric generalized likelihood ratio test is also proposed to check if a non‐parametric coefficient can be simplified as a parametric one. A conditional bootstrap version is suggested to approximate the distribution of the test under the null hypothesis. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed methods. We further apply the proposed model and methods to a data set from a human visceral Leishmaniasis study conducted in Brazil from 1994 to 1997. Numerical results outperform the traditional generalized linear model and the proposed GACM is preferable.