Various effects have been made to remedy the curse ofdimensionality for high-dimensional data. Partiallylinear models, as an effective dimensional reductiontechnique, have been intensively studied inliterature. We develop methodology for the estimationof regression parameters in partially linear modelswhen the covariates are measured with errors or maybe missing. We are particularly concerned with twocases where we observe a surrogate of the covariate.The second case focuses on the linear covariatebeing incompletely observable. We give thecorresponding solutions for the above problems. Thefirst solution employs the technique of correctingfor attenuation. The second is proposed using inverseweight probability. The resulting estimators areproven to be asymptotically normal. The model is usedto analyze a data set from the Framingham Heart Studyfor the purpose of illustrating the methods. We alsoinvestigate the semiparametric partially linearsingle index errors-in-variables models, for whichtwo classes of estimators are proposed, and thecorresponding theoretical properties are derived andcompared.

Business & Money

Liang, Hua

Education & Reference

VDM Verlag

<p>In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.</p>

Partially Linear Models (Contributions to Statistics)

Härdle, Wolfgang

Gao, Jiti

Economics

Physica

survey local people s congresses Introduction [Paperback](Chinese Edition)

democracy and legal system in China Press

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