Miscellanea. Surprising effects of measurement error on an aggregate data estimator
在Probit回归中，当每个研究的观测数很大时，正态分布加性测量误差不会导致衰减，反而使渐近偏差远离零假设，这是首个已知的反向衰减案例。
In a generalised linear model with a single, normally distributed covariate, for the most part the effect of normally distributed additive measurement error is attenuation, i.e. asymptotic bias towards the null. Prentice & Sheppard (1995) suggested a marginalised random effects approach to combining the results of different studies on binary outcomes. We show that, in probit regression, when the number of observations per study is large, under the stated normality assumptions attenuation never occurs. In fact, the asymptotic bias is away from the null. This appears to be the first known case under reasonable distributional assumptions that the effect of measurement error is reverse-attenuation.