Dimension reduction in a semiparametric regression model with errors in covariates
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In this paper, the authors consider a semiparametric estimation method for general regression models when some of the predictors are measured with error, and they show that the usual theory is essentially as good as one can do with this technique.Abstract:
We consider a semiparametric estimation method for general regression models when some of the predictors are measured with error. The technique relies on a kernel regression of the "true" covariate on all the observed covariates and surrogates. This requires a nonparametric regression in as many dimensions as there are covariates and surrogates. The usual theory copes with such higher-dimensional problems by using higher-order kernels, but this is unrealistic for most problems. We show that the usual theory is essentially as good as one can do with this technique. Instead of regression with higher-order kernels, we propose the use of dimension reduction techniques. We assume that the "true" covariate depends only on a linear combination of the observed covariates and surrogates. If this linear combination were known, we could apply the one-dimensional versions of the semiparametric problem, for which standard kernels are applicable. We show that if one can estimate the linear directions at the root-$n$ rate, then asymptotically the resulting estimator of the parameters in the main regression model behaves as if the linear combination were known. Simulations lend some credence to the asymptotic results.read more
Citations
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References
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Book
Measurement Error Models
TL;DR: In this paper, the authors provide a complete treatment of an important and frequently ignored topic, namely measurement error models, including regression models with errors in the variables, latent variable models, and factor models.
Journal ArticleDOI
Projection Pursuit Regression
TL;DR: In this article, a nonparametric multiple regression (NMM) method is presented, which models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner.
Journal ArticleDOI
Sliced Inverse Regression for Dimension Reduction
TL;DR: In this article, sliced inverse regression (SIR) is proposed to reduce the dimension of the input variable without going through any parametric or nonparametric model-fitting process.
Book
Transformation and Weighting in Regression
Raymond J. Carroll,David Ruppert +1 more
TL;DR: The Transform-Both-Sides Methodology as mentioned in this paper combines Transformations and Weighting for least square estimation and inference for Variance Functions, which has been applied to generalized least squares and the analysis of heteroscedasticity.
Journal ArticleDOI
Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error
TL;DR: Two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random (unbiased) within-person variation or to systematic errors for individual subjects.
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