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June 10, 2026

Sufficient and necessary conditions for strong consistency of LS estimators in simple linear EV regression models based on m-WOD errors

Key Points

This research aims to establish conditions for strong consistency of LS estimators in linear EV regression models.
Derived sufficient and necessary conditions for LS estimators using techniques like SLLN and truncation methods.
Conducted numerical simulations to support theoretical results.
Analyzed real-data example with diamond prices to demonstrate practical applicability.
The findings confirm that specific conditions lead to strong consistency of LS estimators.
Numerical simulations align with theoretical predictions, validating the model.
Real-data example provides evidence of the model’s relevance in practical scenarios.

Abstract

In this paper, we investigate the strong consistency of the least squares (LS) estimators for the unknown parameters β and θ in a simple linear errors-in-variables (EV) regression model under the assumption of m-widely orthant dependent (m-WOD) random errors. Under weaker conditions, we apply tools such as the strong law of large numbers (SLLN) for randomly weighted sums, truncation techniques, and slicing techniques to derive the sufficient and necessary conditions for the strong consistency. Numerical simulations are conducted to validate our theoretical findings. Additionally, we analyze a real-data example analyzing of diamond prices dataset, and the results demonstrate the practical relevance and applicability of the proposed theory.

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Sufficient and necessary conditions for strong consistency of LS estimators in simple linear EV regression models based on m-WOD errors

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