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A comparative study of linear regression methods in noisy environments
Author(s) -
Reis Marco S.,
Saraiva Pedro M.
Publication year - 2004
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.897
Subject(s) - computer science , heteroscedasticity , noise (video) , raw data , focus (optics) , linear regression , metrology , instrumentation (computer programming) , data mining , multivariate statistics , regression , econometrics , statistics , machine learning , mathematics , artificial intelligence , physics , optics , image (mathematics) , programming language , operating system
With the development of measurement instrumentation methods and metrology, one is very often able to rigorously specify the uncertainty associated with each measured value (e.g. concentrations, spectra, process sensors). The use of this information, along with the corresponding raw measurements, should, in principle, lead to more sound ways of performing data analysis, since the quality of data can be explicitly taken into account. This should be true, in particular, when noise is heteroscedastic and of a large magnitude. In this paper we focus on alternative multivariate linear regression methods conceived to take into account data uncertainties. We critically investigate their prediction and parameter estimation capabilities and suggest some modifications of well‐established approaches. All alternatives are tested under simulation scenarios that cover different noise and data structures. The results thus obtained provide guidelines on which methods to use and when. Interestingly enough, some of the methods that explicitly incorporate uncertainty information in their formulations tend to present not as good performances in the examples studied, whereas others that do not do so present an overall good performance. Copyright © 2005 John Wiley & Sons, Ltd.