Efficient semiparametric estimation in generalized partially linear additive models

Yu, Kyusang; Lee, Young Kyung

doi:10.1016/j.jkss.2010.02.001

“…The proofs of these theorems are given in the Appendix. It is worthwhile pointing out that taking the additive structure of the nuisance parameter into account leads to a smaller asymptotic variance than that of the estimators which ignore the additivity [Yu and Lee (2010)]. Carroll et al (2009) had the same observation for a special case with repeated measurement data when g is the identity function.…”

Section: Assumptions and Asymptotic Resultsmentioning

confidence: 84%

Estimation and variable selection for generalized additive partial linear models

Wang¹,

Liu²,

Liang³

et al. 2011

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We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration.

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“…Yu et al (2008), and Yu and Lee (2010), respectively, discussed fitting GAM(generalized additive models) and by kernel smoothing. Although the kernel smoothing techniques of fitting GAM and GPLAM have very nice theoretical properties, they are known to be computationally expensive in a high-dimension.…”

Section: Generalized Partially Linear Additive Modelmentioning

confidence: 99%

“…The smooth backfitting technique proposed by Mammen et al (1999) is known as a powerful technique for fitting structured nonparametric models. Yu and Lee (2010) studied smooth backfitting with profiling as a way of fitting the model under study; however, its practical implementation is computationally quite expensive. In addition, Yu and Lee (2010) failed to give numerical properties of the method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Partially Linear Additive Models for Credit Scoring

Shim¹,

Lee

²

2011

Korean Journal of Applied Statistics

1

0

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Credit scoring is an objective and automatic system to assess the credit risk of each customer. The logistic regression model is one of the popular methods of credit scoring to predict the default probability; however, it may not detect possible nonlinear features of predictors despite the advantages of interpretability and low computation cost. In this paper, we propose to use a generalized partially linear model as an alternative to logistic regression. We also introduce modern ensemble technologies such as bagging, boosting and random forests. We compare these methods via a simulation study and illustrate them through a German credit dataset.

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“…It is worthwhile pointing out that taking the additive structure of the nuisance parameter into account leads to a smaller asymptotic variance than that of the estimators which ignore the additivity [Yu and Lee (2010)]. Carroll et al (2009) had the same observation for a special case with repeated measurement data when g is the identity function.…”

Section: Estimation Methodsmentioning

confidence: 98%

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Wang

¹

,

Liu²,

Liang³

et al.

18

0

View full text Add to dashboard Cite

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration.

show abstract

Efficient semiparametric estimation in generalized partially linear additive models

Cited by 10 publications

References 14 publications

Estimation and variable selection for generalized additive partial linear models

Estimation and variable selection for generalized additive partial linear models

Generalized Partially Linear Additive Models for Credit Scoring

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