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Linear structural error-in-variables models with univariate observations arerevisited for studying modified least squares estimators of the slope andintercept. New marginal central limit theorems (CLT's) are established forthese estimators, assuming the existence of four moments for the measurementerrors and that the explanatory variables are in the domain of attraction ofthe normal law. The latter condition for the explanatory variables is used thefirst time, and is so far the most general in this context. It is also optimal,or nearly optimal, for our CLT's. Moreover, due to the obtained CLT's being inStudentized and self-normalized forms to begin with, they are a priori nearly,or completely, data-based, and free of unknown parameters of the jointdistribution of the error and explanatory variables. Consequently, they lead toa variety of readily available, or easily derivable, large-sample approximateconfidence intervals (CI's) for the slope and intercept. In contrast, inrelated CLT's in the literature so far, the variances of the limiting normaldistributions, in general, are complicated and depend on various, typicallyunknown, moments of the error and explanatory variables. Thus, thecorresponding CI's for the slope and intercept in the literature, unlike thoseof the present paper, are available only under some additional modelassumptions.

Central limit theorems in linear structural error-in-variables models with explanatory variables in the domain of attraction of the normal law