Estimation in partially linear models

Eubank, R. L.; Kambour, E. L.; Kim, J. T.; Klipple, K.; Reese, C. Shane; Schimek, Michael G.

doi:10.1016/s0167-9473(98)00054-1

Cited by 45 publications

(11 citation statements)

References 9 publications

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“…Buckley et al (1988) considered a wide class of estimators of the residual variance in nonparametric regression and derived the minimax mean squared error estimator over a natural class of regression curve. Eubank et al (1998) and Klipple and Eubank (2007) extended work from Gasser et al (1986) to partially linear models. Lu (2014) extends the variance estimator from Gasser et al (1986) by incorporating survey weights to nonparametric regression in complex surveys and derived the asymptotic properties.…”

Section: Consider a General Nonparametric Regression Modelmentioning

confidence: 99%

Adjusted Confidence Bands for Complex Survey Data

Zhang

Gong

Cheng

2016

Communications in Statistics - Simulation and Computation

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Confidence bands in nonparametric regression have been studied for a long time with data assumed to be generated from independent and identically distributed (iid) random variables. The methods and theoretical results for iid data, however, do not directly apply to data from stratified multistage samples. In this paper, we extend the confidence bands introduced by Zhang and Lu (2008) for iid case to complex surveys based on an entirely data-driven procedure; the proposed confidence bands incorporate both the sampling weights and the kernel weights. Simulation studies show that the proposed method works well.

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Section: Consider a General Nonparametric Regression Modelmentioning

confidence: 99%

Adjusted Confidence Bands for Complex Survey Data

Zhang

Gong

Cheng

2016

Communications in Statistics - Simulation and Computation

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“…Proof: Transforming y and X in model (1), to y = (I − S) y and X = (I − S) X (see Speckman 1988, Eubank et al 1998, Schimek 2000, applying RLSE for linear models and (5) we get the thesis.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…In this paper we do not consider the problem of choosing the smoothing parameter. Some methods of doing this may be found in Durban et al (2003), Eubank et al (1998), andSchimek (2000).…”

Section: Introductionmentioning

confidence: 99%

Constrained estimators of treatment parameters in semiparametric models

Przystalski

Krajewski

2007

Statistics & Probability Letters

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“…First, recall that the PLS estimator stated in (7) is a pointwise kill-or-shrink estimator, where each estimate is either thresholded or shrunk toward zero by a certain amount, depending on the penalty [see (7) in Theorem 1]. At convergence of the backfitting procedure, one can legitimately assume that , as defined in (8), will stabilize at .…”

Section: ) Parametric Inferencementioning

confidence: 99%

Penalized partially linear models using sparse representations with an application to fMRI time series

Fadili

Bullmore

2005

IEEE Trans. Signal Process.

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Abstract-In this paper, we consider modeling the nonparametric component in partially linear models (PLMs) using linear sparse representations, e.g., wavelet expansions. Two types of representations are investigated, namely, orthogonal bases (complete) and redundant overcomplete expansions. For bases, we introduce a regularized estimator of the nonparametric part. The important contribution here is that the nonparametric part can be parsimoniously estimated by choosing an appropriate penalty function for which the hard and soft thresholding estimators are special cases. This allows us to represent in an effective manner a broad class of signals, including stationary and/or nonstationary signals and avoids excessive bias in estimating the parametric component. We also give a fast estimation algorithm. The method is then generalized to handle the case of overcomplete representations. A large-scale simulation study is conducted to illustrate the finite sample properties of the estimator. The estimator is finally applied to real neurophysiological functional magnetic resonance imaging (MRI) data sets that are suspected to contain both smooth and transient drift features.

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Estimation in partially linear models

Cited by 45 publications

References 9 publications

Adjusted Confidence Bands for Complex Survey Data

Adjusted Confidence Bands for Complex Survey Data

Constrained estimators of treatment parameters in semiparametric models

Penalized partially linear models using sparse representations with an application to fMRI time series

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