Application of the iterated weighted least-squares fit to counting experiments

Deming least-squares fit to multiple hyperplanes

A method is derived to fit a set of multidimensional experimental data points having a priori uncertainties and possibly also covariances in all coordinates to a straight line, plane, or hyperplane of any dimensionality less than the number of coordinates. The least-squares formulation used is that of Deming, which treats all coordinates on an equal basis. Experimentalists needing to fit a line...

Resurrecting Weighted Least Squares

This paper shows how asymptotically valid inference in regression models based on the weighted least squares (WLS) estimator can be obtained even when the model for reweighting the data is misspecified. Like the ordinary least squares estimator, the WLS estimator can be accompanied by heterokedasticty-consistent (HC) standard errors without knowledge of the functional form of conditional hetero...

The least squares fit of a hyperplane to uncertain data

Weighted Least Squares and Adaptive Least Squares: Further Empirical Evidence

This paper compares ordinary least squares (OLS), weighted least squares (WLS), and adaptive least squares (ALS) by means of a Monte Carlo study and an application to two empirical data sets. Overall, ALS emerges as the winner: It achieves most or even all of the efficiency gains of WLS over OLS when WLS outperforms OLS, but it only has very limited downside risk compared to OLS when OLS outper...

Weighted total least squares formulated by standard least squares theory

This contribution presents a simple, attractive, and exible formulation for the weighted total least squares (WTLS) problem. It is simple because it is based on the well-known standard least squares theory; it is attractive because it allows one to directly use the existing body of knowledge of the least squares theory; and it is exible because it can be used to a broad eld of applications in t...