Geometric View of Measurement Errors

TL;DR

This paper presents a geometric perspective on measurement errors, analyzing the polynomial nature of slope estimators and comparing their bias and mean squared error through simulations.

Contribution

It introduces a geometric framework for understanding measurement errors and evaluates various slope estimators, including a novel adjusted fourth moment estimator.

Findings

The polynomial of degree four relates to the slope estimator.

Simulation shows improved bias and MSE with the new estimators.

The geometric view provides insights into estimator performance.

Abstract

The slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of various slope estimators for the measurement error model including an adjusted fourth moment estimator introduced by Gillard and Iles (2005) to remove the jump discontinuity in the estimator of Copas (1972). The polynomial of degree four is associated with a minimun deviation estimator. A simulation study compares these estimators showing improvement in bias and mean squared error.