Robust regression methods have advantages over classical least-squares (LS) regression if the strict model assumptions used for LS regression are violated. We briefly review LMS and LTS regression as robust alternatives to LS regression, and illustrate their advantages. Furthermore, it is demonstrated how robust regression can be used if the response variable contains relative rather than absol...

In this second recitation, we will address the following topics: • Review of the projection theorem. • Derivation of the projection operator on the range of a matrix, using completion of squares. • Solutions of under and over constrained linear equations. Notice that this recitation note is an alternative discussion of the least-squares problem which is more difficult than the one you can find ...

We establish an a-posteriori error estimate, with corresponding bounds, that is valid for any FOSLS L-minimization problem. Such estimates follow almost immediately from the FOSLS formulation, but they are usually difficult to establish for other methodologies. We present some numerical examples to support our theoretical results. We also establish a local a-priori lower error bound that is use...

A nonparametric regression model proposed in [Pelletier and Frouin, Applied Optics, 2006] as a solution to the geophysical problem of ocean color remote sensing is studied. The model, called ridge function field, combines a regression estimate in the form of a superposition of ridge functions, or equivalently a neural network, with the idea pertaining to varyingcoefficients models, where the pa...

Examining the correlation between trade and income cannot identify the direction of causation between the two. Countries’ geographic characteristics, however, have important effects on trade, and are plausibly uncorrelated with other determinants of income. This paper therefore constructs measures of the geographic component of countries’ trade, and uses those measures to obtain instrumental va...

In this contribution we consider the popular widelaning technique from the viewpoint of ambiguity decorrelation. It enables us to cast the technique into the framework of the least-squares ambiguity decorrelation adjustment (LAMBDA) and to analyse its relative merits. In doing so, we will provide answers to the following three questions. Does the widelane decorrelate? Does it explicitly appear ...

Thanks to (1.1), the bilinear form on X×X at the left hand side is bounded, symmetric, and elliptic, and the right-hand side defines a bounded functional on X . From the Lax-Milgram lemma, we conclude that (1.2), and so the least-squares problem, has a unique solution u∈X that depends continuously on f ∈Y ′. Whenever the equation Gu= f has a solution, i.e., f ∈IG (consistency), it is the unique...

This paper gives the 2010 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of tha...

A nonlinear regression model with correlated, normally distributed errors is investigated. The bias and the mean square error matrix of the approximate least squares estimator of regression parameters are derived and their limit properties are studied.