Plug-in bandwidth choice in partial linear models with autoregressive errors

Aneiros, Germán; Quintela-del-Rı́o, Alejandro

doi:10.1016/s0378-3758(01)00094-5

Cited by 14 publications

(8 citation statements)

References 29 publications

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“…A number of bandwidth selection methods have been proposed. [21][22][23][24][25] Optimal bandwidths were determined through simulation, in which reference spectra were used as a basis for generating simulated composite spectra. Simulated Raman Spectra Calculations.…”

Section: Methodsmentioning

confidence: 99%

Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

Sowa

Smith²,

Kendall³

et al. 2006

Appl Spectrosc

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Identification and quantification of molecular species are central applications of molecular spectroscopy. In complex multicomponent systems like tissue samples, linear parametric models are often used to estimate the relative concentrations of the biochemical components of the sample. In situations where not all of the components of the sample are known or modeled, such parametric models can suffer from omitted variable bias and result in skewed estimates of component concentrations. We propose a semi-parametric approach that tries to avoid this omitted variable bias by effectively including unknown covariates as a non-parametric term in the regression equation. Constituent concentrations estimated with such partial linear models should outperform strict parametric linear models when the user has limited information on the composition of a multi-constituent system.

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Section: Methodsmentioning

confidence: 99%

Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

Sowa

Smith²,

Kendall³

et al. 2006

Appl Spectrosc

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“…Gao [15] considered the estimation problem of model (1.1) with MA(1) error process. Furthermore, Aneiros-Pérez and Quintela [21] and Aneiros-Pérez, González-Manteiga and Vieu [22], among others, have studied the estimation problem of model (1.1) with serially correlated errors. One interesting case is to consider that the errors are modeled by an autoregressive process with random coefficient of first order.…”

Section: Introductionmentioning

confidence: 99%

“…Gao considered the estimation problem of model with MA(∞) error process. Furthermore, Aneiros‐Pérez and Quintela and Aneiros‐Pérez, González‐Manteiga and Vieu , among others, have studied the estimation problem of model with serially correlated errors.…”

Section: Introductionmentioning

confidence: 99%

L₁penalty and shrinkage estimation in partially linear models with random coefficient autoregressive errors

Fallahpour

Ahmed

Doksum

2011

Appl Stoch Models Bus & Ind

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In partially linear models, we consider methodology for simultaneous model selection and parameter estimation with random coefficient autoregressive errors by using lasso and shrinkage strategies. We provide natural adaptive estimators that significantly improve upon the classical procedures in the situation where some of the predictors are nuisance variables that may or may not affect the association between the response and the main predictors. In the context of two competing partially linear regression models (full and submodels), we consider an adaptive shrinkage estimation strategy and propose the shrinkage estimator and the positive‐rule shrinkage estimator. We develop the properties of these estimators by using the notion of asymptotic distributional risk. The shrinkage estimators are shown to have a higher efficiency than the classical estimators for a wide class of models. For the lasso‐type estimation strategy, we devise efficient algorithms to obtain numerical results. We compare the relative performance of lasso with the shrinkage estimator and the other estimators. Monte Carlo simulation experiments are conducted for various combinations of the nuisance parameters and sample size, and the performance of each method is evaluated in terms of simulated mean squared error. The comparison reveals that lasso and shrinkage strategies outperform the classical procedure. The relative performance of lasso and shrinkage strategies is comparable. The shrinkage estimators perform better than the lasso strategy in the effective part of the parameter space when, and only when, there are many nuisance variables in the model. A data example is showcased to illustrate the usefulness of suggested methods. Copyright © 2011 John Wiley & Sons, Ltd.

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“…In recent years, this model has gained a lot of attention in order to explore the nature of complex nonlinear phenomena. This model has been widely studied in the literature see for example [16], [5], [1] among others. The partially linear models allow modeling the response variable with a set of predictors that enter linearly in the model while one of them is considered in the model nonparametrically.…”

Section: Introductionmentioning

confidence: 99%

Partially linear models on Riemannian manifolds

González–Manteiga¹,

Henry²,

Rodríguez³

2010

Preprint

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In partially linear models the dependence of the response y on (x t , t) is modeled through the relationship y = x t β + g(t) + ε where ε is independent of (x t , t). In this paper, estimators of β and g are constructed when the explanatory variables t take values on a Riemannian manifold. Our proposal combine the flexibility of these models with the complex structure of a set of explanatory variables. We prove that the resulting estimator of β is asymptotically normal under the suitable conditions. Through a simulation study, we explored the performance of the estimators. Finally, we applied the studied model to an example based on real dataset.

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Plug-in bandwidth choice in partial linear models with autoregressive errors

Cited by 14 publications

References 29 publications

Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

L₁penalty and shrinkage estimation in partially linear models with random coefficient autoregressive errors

Partially linear models on Riemannian manifolds

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Plug-in bandwidth choice in partial linear models with autoregressive errors

Cited by 14 publications

References 29 publications

Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

L1penalty and shrinkage estimation in partially linear models with random coefficient autoregressive errors

Partially linear models on Riemannian manifolds

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L₁penalty and shrinkage estimation in partially linear models with random coefficient autoregressive errors