Polynomial Regression With Errors in the Variables

Abstract

A polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coef®cients, assuming hypothetically the latent true regressor variable to be known, and then adjusting for the errors. If normality of the error variables can be assumed, the estimator can be simpli®ed considerably. Only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known. If the variance of the errors in the dependent variable is also known, another estimator can be constructed.

Consistent estimation in the bilinear multivariate errors-in-variables model

“…Indeed, as mentioned in [Ful87], adding correction matrices DA, DB and DC of minimal Frobenius norm in order to make ðA À DAÞX ðB À DBÞ ¼ C À DC compatible results in biased estimates for the parameter X. In this paper an adjusted least squares (ALS) estimator [CRS95,CS98] of X is presented and shown to be consistent.…”

Some recent advances in measurement error models and methods

“…If they exist, then ψ CS = yf 1 − f 2 . In the polynomial model one can construct polynomials t r (x) of degree r such that E [t r (x)|ξ] = ξ r Schneeweiss, 1998, andCheng et al, 2000). The corrected score function is then given by…”

Different Nonlinear Regression Models with Incorrectly Observed Covariates

“…For i = 1 : : : n it holds that W i = X i + U i with U i N(0 2 i ) where Cov ( U i U j ) = 0 for i 6 = j j = 1 : : : n and the errors U i are independent from the variables Y i , X i and Z i : (5) This implies that the measurement errors are nondi erential. For some applications the assumption of a heteroscedastic measurement error model is more reasonable than to assume constant error variances.…”