Measurement Error Regression with Unknown Link: Dimension Reduction and Data Visualization
作者:
RaymondJ. Carroll,
Ker-Chau Li,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1992)
卷期:
Volume 87,
issue 420
页码: 1040-1050
ISSN:0162-1459
年代: 1992
DOI:10.1080/01621459.1992.10476259
出版商: Taylor & Francis Group
关键词: Data visualization;Dimension reduction;Errors in variables;Generalized linear model;Logistic regression;Sliced inverse regression
数据来源: Taylor
摘要:
A general nonlinear regression problem is considered with measurement error in the predictors. We assume that the response is related to an unknown linear combination of a multidimensional predictor through anunknownlink function. Instead of observing the predictor, we instead observe a surrogate with the property that its expectation is linearly related to the true predictor with constant variance. We identify an important transformation of the surrogate variable. Using this transformed variable, we show that if one proceeds with the usual analysis ignoring measurement error, then both ordinary least squares and sliced inverse regression yield estimates which consistently estimate the true regression parameter, up to a constant of proportionality. We derive the asymptotic distribution of the estimates. A simulation study is conducted applying sliced inverse regression in this context.
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