The Method of Least Squares and Some Alternatives.

Identification of Outliers

“…The genesis of research into outlier rejection is bound up with that of the method of least squares, and the very extensive history of least squares given by Harter ( 1974Harter ( , 1975Harter ( , 1976 contains a full discussion of early writings on outlier rejection. Another account of the literature up to 1931 is to be found in Rider ( 1933), and so it is appropriate to outline only a few major discoveries and concepts, up to the major paper by Pearson and Chandra Sekar ( 19 36 ).…”

Array Algorithms for H 2 and H ∞ Estimation

“…3 The numerical advantages of the square-root transformations arise from the length preserving properties of unitary transformations, and from the fact that the dynamic range of the entries in P 1=2 j is roughly the square-root of the dynamic range of those in P j . Moreover, regular computational (systolic) arrays can be designed to implement sequences of elementary unitary transformations 22].…”

“…We can summarize the above discussion as follows. 3 The above square-root method is closely related to the QR (factorization) method for solving systems of linear equations. where j is any unitary matrix that triangularizes the above pre-array.…”

“…The rst array forms for the Kalman lter are called the square-root array algorithms and were devised in the late 1960's 1, 2,3 ]. These algorithms are closely related to the (so-called) QR method for solving systems of linear equations 4,5,6,7], and have the properties of better conditioning, reduced dynamical range, and the use of orthogonal transformations, which typically lead to more stable algorithms.…”

Robust methods in econometrics

“…See Huber (1972) and Harter (1974). Indeed there were serious debates among such 18th century luminaries as Laplace, Legendre and Gauss on appropriate statistical models and estimation methods for astronomical data.…”