소표본 errors-in-vairalbes 모형에서의 통계 추론

Small-Sample Inference in the Errors-in-Variables Model

We consider the semiparametric linear errors-in-variables model: yi=(<TEX>${alpha}+{eta}ui+{varepsilon}i$</TEX>, xi=ui＋<TEX>${varepsilon}i$</TEX> i=1, …, n where (xi, yi) stands for an observation vector, (ui) denotes a set of incidental nuisance parameters, (<TEX>${alpha}$</TEX> , <TEX>${eta}$</TEX>) is a vector of regression parameters and (<TEX>${varepsilon}i$</TEX>, <TEX>${delta}i$</TEX>) are mutually uncorrelated measurement errors with zero mean and finite variances but otherwise unknown distributions. On the basis of a simple small-sample low-noise a, pp.oximation, we propose a new method of comparing the mean squared errors(MSE) of the various competing estimators of the true regression parameters ((<TEX>${alpha}$</TEX> , <TEX>${eta}$</TEX>). Then we show that a class of estimators including the classical least squares estimator and the maximum likelihood estimator are consistent and first-order efficient within the class of all regular consistent estimators irrespective of type of measurement errors.