Robust estimator for correlated observations based on bifactor equivalent weights

A new robust parameter estimator for the adjustment of correlated observations is developed based on a 'bifactor reduction' model of weight elements. A shrinking factor for weight elements is proposed. The new equivalent weight matrix composed by the bifactor weight elements preserves the symmetry and keeps the original correlation coefficients unchanged. The new parameter estimator with its error influence function is derived. The robustness and efficiency of the new robust estimator is demonstrated with a simulated example and some conclusions are drawn.