Mean squared error of James–Stein estimators for measurement error models

Whittemore (1989) in an interesting paper considered estimation of regression coefficients in measurement error models. She had the very interesting result which showed how to overcome the inconsistency of the usual least squares estimator of the regression coefficient in a measurement error model by an alternative James–Stein (James and Stein, 1961) estimator. The author did not provide a rigorous proof for the consistency of the suggested estimator, nor did she provide MSE of her estimator. Our objective is to provide a rigorous second order expansion of the mean squared error of the proposed James–Stein estimator under both known measurement variance and unknown measurement variance.