What question did this study set out to answer?

This paper aims to establish conditions under which least squares estimators are consistent or asymptotically normal in linear regression models.

Asymptotic Normality and Consistency of the Least Squares Estimators for Families of Linear Regressions

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Randomized trial investigates least squares estimators in linear regressions, suggesting new conditions for consistency and normality.

This paper aims to establish conditions under which least squares estimators are consistent or asymptotically normal in linear regression models.
Analyzed families of linear regressions with error variables being uncorrelated or independent.
Developed conditions on error distribution functions and regression variables to ensure consistent estimators.
Used central limit theorem principles to derive results about parameter spaces.
Theorem 1 demonstrates that consistency of least squares estimators is achieved under mild conditions on error distributions.
Theorem 2 reveals that least squares estimators are asymptotically normal for independent error sequences, proving its relation to the central limit theorem.
Both theorems hold for a broad range of practical regression problems, without requiring knowledge of specific error sequences.

Friedhelm Eicker (1963) studied this question.

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