| Abstract: |
The numerical effect of measurement error on the least squares estimate in the linear regression model is examined. The change in the least squares estimate is measured by calculating a stochastic upper bound on the relative distance between the true (unobserved) and observed (with error) jth component. The bound is derived in the case of k of p explanatory variables measured with error. If the bound indicates that none of the estimates are badly perturbed, the analysis can continue without concern about the effect of measurement error. Simulations are carried out to compare this bound with the first-order upper bound of Golub and Van Loan [Matrix Computations, Johns Hopkins University Press, 1983], and the componentwise upper bound of Higham [Contemp. Math., 112 (1990), pp. 195-208]. |
