We consider the problem of locating a user’s position from a set of noisy pseudoranges to a group of satellites. We consider both the nonlinear least squares formulation of the problem, which is nonconvex and nonsmooth, and the nonlinear squared least squares variant, in which the objective function is smooth, but still nonconvex. We show that the squared least squares problem can be reformulat...

One of the most commonly used methods for the analysis of experimental data in the biochemical literature is nonlinear least squares (regression). This group of methods are also commonly misused. The purpose of this article is to review the assumptions inherent in the use of least-squares techniques and how these assumptions govern the ways that least-squares techniques can and should be used. ...

abstract In this paper we introduce certain numbers, called collinearity indices, which are useful in detecting near collinearities in regression problems. The coeecients enter adversely into formulas concerning signiicance testing and the eeects of errors in the regression variables. Thus they provide simple regression diagnostics, suitable for incorporation in regression packages.

We revisit compressed least squares (CLS) regression as originally analyzed in Maillard and Munos (2009) and later on in Kaban (2014) with some refinements. Given a set of high-dimensional inputs, CLS applies a random projection and then performs least squares regression based on the projected inputs of lower dimension. This approach can be beneficial with regard to both computation (yielding a...

Number of latents The same number of factors will be extracted for PLS responses as for PLS factors. The researcher must specify how many latents to extract (in SPSS the default is 5). There is no one criterion for deciding how many latents to employ. Common alternatives are: 1. Cross-validating the model with increasing numbers of factors, then choosing the number with minimum prediction error...

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