Consistent covariate selection and post model selection inference in semiparametric regression

By Florentina Bunea. 2004

82 citations recorded by the source corpus.

This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models, we can consistently estimate the subset of nonzero coefficients of the linear part. Moreover, the selected estimator of the linear component is asymptotically normal.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Sparse Partially Linear Additive Models (2014, methodology): “For example, in Bunea (2004), Xie and Huang (2009), and Müller and van de Geer (2015), methods are developed to perform feature selection for the set L while assuming that the set N is known; Lian and Liang (2013) and Wang et al. (2014) performed feature selection on both L and N individually but…”
On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection (2006, background): “(This argument has been adopted in, e.g., Bunea 2004; Dufour, Pelletier, and Renault 2003, sec.”
SPADES AND MIXTURE MODELS (2009, methodology): “the cross-validated loss function via a BICtype penalty is motivated by the known properties of the BIC-type criteria to yield consistent model selection in a large array of models; see, for example, [7] for results on regression models. The numerical experiments presented below show that this is al”
Sparse estimators and the oracle property, or the return of Hodges’ estimator (2007, unknown): “In a recent paper, Bunea (2004) uses such procedures in a semiparametric framework and emphasizes the oracle property of the resulting estimator; see also Bunea and McKeague (2005). At first sight, the oracle property appears to be a desirable property of an estimator as it seems to guarantee that, ”
On the distribution of the adaptive LASSO estimator (2008, unknown): “, Bunea (2004), Bunea & McKeague (2005), Fan & Li (2002, 2004), Li & Liang (2007), Wang & Leng (2007), Wang, G. Li and Jiang (2007), Wang, G. Li and Tsai (2007), Wang, R. Li and Tsai (2007), Yuan & Lin (2007), Zhang & Lu (2007), Zou & Yuan (2008), Zou & Li (2008), Johnson et al. (2008)). The ‘oracle”
Model Selection (2018, background): “…estimator and that one can estimate θ asymptotically as efficient as if knowledge about the minimal true model were available: Two prominent examples are Bunea (2004) and Fan and Li (2001) who advertise this property of their estimators, the latter reference dubbing this property the ‘oracle…”
Tuning parameter selectors for the smoothly clipped absolute deviation method. (2007, methodology): “In the context of partially linear models, Bunea (2004) and Bunea & Wegkamp (2004) proposed an information-type criterion and established a consistency property. Fan & Li (2004) extended their nonconvex penalised least squares method to partially linear models with longitudinal data, and showed that”
An asymptotic theory for model selection inference in general semiparametric problems (2007, unknown): “An exception is Bunea (2004) who studies post model selection inference in, again, partially linear regression models using penalized least squares estimation in combination with a construction of sieves.”
Aggregation for Gaussian regression (2007, methodology): “Bounds of the type (1.4) in regression problems have been obtained by many authors mainly for the model selection case; see, for example, [4, 5, 7, 8, 9, 10, 11, 12 , 15, 23, 28, 30, 32, 42] and the references cited in these works.”
Statistical Estimation in Generalized Multiparameter Likelihood Models (2009, methodology): “Bunea (2004) constructed a penalized least squares criterion for variable selection in the linear part of a partially linear model. For a generalized varying-coefficient partially linear model, Li and Liang (2008) used a nonconcave penalized likelihood to select significant variables in the parametr”
SHRINKAGE, PRETEST AND ABSOLUTE PENALTY ESTIMATORS IN PARTIALLY LINEAR MODELS (2007, background): “Some recent work on semiparametric models can be found in Wang, Linton & Härdle (2004), Xue, Lam & Gouying (2004), Liang et al. (2004), and Bunea (2004).”