BOOTSTRAP INFERENCE IN SEMIPARAMETRIC GENERALIZED ADDITIVE MODELS
By Wolfgang Karl Härdle, Sylvie Huet, Enno Mammen, Stefan Sperlich. Econometric Theory, 2004
114 citations recorded by the source corpus.
Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y |X;T) = G{XTβ + α + m1(T1) + ··· + md(Td)}. Here, G is a known link, α and β are unknown parameters, and m1,…,md are unknown (smooth) functions of possibly higher dimensional covariates T1,…,Td. Estimates of m1,…,md, α, and β are presented, and asymptotic distributions are given for both the nonparametric and the parametric part. The main focus of the paper is application of bootstrap methods. It is shown how bootstrap can be used for bias correction, hypothesis testing (e.g., component-wise analysis), and the construction of uniform confidence bands. Further, bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of the methods is illustrated in a simulation study.This research was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373 “Quantifikation und Simulation ökonomischer Prozesse,” Humboldt-Universität zu Berlin, DFG project MA 1026/6-2, the Spanish “Dirección General de Enseñanza Superior,” no. BEC2001-1270, and the grant “Nonparametric methods in finance and insurance” from the Danish Social Science Research Council. We thank Marlene Müller, Oliver Linton, and two anonymous referees for helpful discussion.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e917eac199466aaea6f98dae1d31b4d5ab670508
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- Giampiero Marra
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Citations in the corpus
- Coverage Properties of Confidence Intervals for Generalized Additive Model Components (2012, methodology): “Alternatively using (4) we have Ê(M) = 1 + ‖ √ CX(Fβ̂ − β̂)‖(2)/n, (11) and combining this with estimator (5) yields intervals f̂(xi)− Ê(B) √”
- Semiparametric inference in generalized mixed effects models (2008, methodology): “Liu (1988) studied the wild bootstrap under regression models with non-IID observations, and Härdle et al. (2004) discussed various bootstrap methods for doing inference in generalized partial linear additive models.”
- Efficient and fast spline-backfitted kernel smoothing of additive models (2009, background): “J. Wang (B) Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA e-mail: wangjing@math.uic.edu L. Yang Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA e-mail: yang@stt.msu.edu”