Least Trimmed Squares Estimator in the Errors-in-Variables Model

Abstract

We propose a robust estimator in the errors-in-variables model using the least trimmed squares estimator. We call this estimator the orthogonal least trimmed squares (OLTS) estimator. We show that the OLTS estimator has the high breakdown point and appropriate equivariance properties. We develop an algorithm for the OLTS estimate. Simulations are performed to compare the efficiencies of the OLTS estimates with the total least squares (TLS) estimates and a numerical example is given to illustrate the effectiveness of the estimate.Breakdown point, equivariance, errors-in-variables model, least trimmed squares estimator, orthogonal regression,

Automatic Surveillance Camera Calibration without Pedestrian Tracking

“…This is analogous to the robust statistics of a truncated quadratic [1] in that it gives constant punishment to samples outside the region of interest, and therefore is robust to noisy sample data with a large proportion of outliers. More importantly, our prior knowledge about human height distribution indicates a meaningful threshold (τ = 10%), which makes this metric more favorable in our framework in comparison with other popular robust statistics such as least trimmed squares [8] that only consider a fixed number of nearest samples. The term 1/µ in equation 12 gives further punishment to larger µ that result in larger regions of interest.…”

On Consistency of Ls Estimators in the Errors-in-Variable Regression Model

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