MEASUREMENT ERROR REGRESSION WITH UNKNOWN LINK - DIMENSION REDUCTION AND DATA VISUALIZATION Academic Article

abstract

• 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 an unknown link 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. 1992 Taylor & Francis Group, LLC.

authors

• Carroll, Raymond

published proceedings

• JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

author list (cited authors)

• CARROLL, R. J., & LI, K. C.

citation count

• 33

complete list of authors

• CARROLL, RJ||LI, KC

publication date

• December 1992

publisher

• Taylor & Francis  Publisher

keywords

• Data Visualization
• Dimension Reduction
• Errors In Variables
• Generalized Linear Model
• Logistic Regression
• Sliced Inverse Regression

Digital Object Identifier (DOI)

• 10.2307/2290641

start page

• 1040

end page

• 1050

volume

• 87

issue

• 420

URL

• http%3A%2F%2Fdx.doi.org%2F10.1080%2F01621459.1992.10476259