Signi cance Regression: Improved Estimation from Collinear Data for the Measurement Error Model

This paper examines improved regression methods for the linear multivariable measurement error model MEM when the data su ers from collinearity The di culty collinearity presents for reliable estimation is discussed and a systematic procedure signi cance regression SR MEM is developed to address collinearity In addition to mitigating collinearity di culties SR MEM produces asymptotically un biased estimates The use of ordinary least squares OLS for the MEM is examined For collinear data OLS can improve the mean squared error of estimation over the maximum likelihood ML unbiased estimator in a manner analogous to ridge re gression RR The signi cance regression method developed for the classical model Author to whom correspondence should be addressed phone fax e mail mm imc caltech edu SR classical can also be used for data with measurement errors SR classical is sim ilar SR MEM and can yield better estimation than the ML estimator for collinear data Numerical examples illustrate several points