Explore chapters and articles related to this topic
S-PLUS
Published in Paul W. Ross, The Handbook of Software for Engineers and Scientists, 2018
Linear least-squares regression is performed in S-PLUS using the linear models function lm. Logistic regression and Poisson regression are two examples of models that are usually fit using the generalized linear models function glm and the generalized additive models function gam. S-PLus functions for doing robust regression include lifit for L1 regression, rreg for M-estimate regression, and ltsreg least trimmed squares regression (includes least median squares regression).
Application of robust estimation in geodesy using the harmony search algorithm
Published in Journal of Spatial Science, 2018
Geodesy deals with the measurement of the earth and in this sense it uses advanced measurement techniques such as GNSS. There are a number of GNSSs in operation (fully or partly): the United States Global Positioning System (GPS), the Russian GLObal’naya NAvigatsionnaya Sputnikovaya Sistema (GLONASS) and the European Galileo system. Using these techniques the coordinates of the points are determined in a chosen coordinate system. GNSS networks are established for this purpose and measurements are made. Once established, GNSS networks may be used by many professions; for example, geodesy, surveying, geology, forestry, environmental engineering, civil engineering, archaeology, agriculture, urban planning, military and probably many more. The classic parameter estimation method used for geodetic measurements (see section 2) is the LS (least squares) method. Yet, to obtain correct results for estimated parameters, it must be ensured that no outliers (gross errors/blunders) are present in the measurements and only the random errors remain. Otherwise, the LS method might provide very poor results. Unfortunately, errors are generally present in the measurement data-set. On the other hand, many RE (robust estimation) methods which are less sensitive against outliers than the LS method have been developed and they can produce more reliable results even if some measurements contain errors (Rousseeuw 1984, Hampel et al. 1986, Huber and Ronchetti 2009, Yetkin and Inal 2011). Robust estimation techniques are created to offer maximum resistance to the influence of errors in the measurements. Thus, robust estimation not only works as a detection tool but also provides the least-affected solution. There are numerous robust methods in use, including least absolute deviations (Edgeworth Edgeworth 1887, Marshall and Bethel 1996, Marshall 2002, Simkooei 2003), M-estimators (Huber 1964), R-estimators (Jaeckel 1972), least trimmed squares (Rousseeuw 1984, Rousseeuw and Leroy 1987), least median squares (Rousseeuw 1984) and sign-constrained robust least squares (Xu 2005, Yetkin and Berber 2013).