RT Journal Article
T1 Empirical likelihood based testing for regression
A1 Keilegom, Ingrid van
A1 Sánchez Sellero, César
A1 González Manteiga, Wenceslao
K1 Marked empirical process
K1 Model check for regression
K1 Nonlinear regression
K1 Partial linear model
K1 Residuals
AB Consider a random vector (X, Y ) and let m(x) = E(Y |X = x).We are interested in testing H0 : m ∈ MΘ,G = {γ(·, θ, g) : θ ∈ Θ, g ∈ G}for some known function γ, some compact set Θ ⊂ IRp and some functionset G of real valued functions. Specific examples of this general hypothesis include testing for a parametric regression model, a generalized linearmodel, a partial linear model, a single index model, but also the selection ofexplanatory variables can be considered as a special case of this hypothesis.To test this null hypothesis, we make use of the so-called marked empirical process introduced by and studied by for the particular caseof parametric regression, in combination with the modern technique of empirical likelihood theory in order to obtain a powerful testing procedure.The asymptotic validity of the proposed test is established, and its finitesample performance is compared with other existing tests by means of asimulation studyTo test this null hypothesis, we make use of the so-called marked empirical process introduced by [4] and studied by [16] for the particular case of parametric regression, in combination with the modern technique of empirical likelihood theory in order to obtain a powerful testing procedure. The asymptotic validity of the proposed test is established, and its finite sample performance is compared with other existing tests by means of a simulation study
PB The Institute of Mathematical Statistics
PB The Bernoulli Society
YR 2008
FD 2008
LK http://hdl.handle.net/10347/18567
UL http://hdl.handle.net/10347/18567
LA eng
NO Van Keilegom, Ingrid; Sánchez Sellero, César; González Manteiga, Wenceslao. Empirical likelihood based testing for regression. Electron. J. Statist. 2 (2008), 581-604. doi:10.1214/07-EJS152
NO Financial support from IAP research networks nr. P5/24 and P6/03 of the Belgian government (Belgian Science Policy) is gratefully acknowledged.Financial support from the Spanish Ministry of Science and Technology (with additional European FEDER support) through project MTM2005-00820
DS Minerva
RD 27 abr 2026