TheMethod of Least Squares
نویسنده
چکیده
The least squaremethods (LSM) is probably themost popular technique in statistics. This is due to several factors. First, most common estimators can be casted within this framework. For example, themean of a distribution is the value that minimizes the sum of squared deviations of the scores. Second, using squares makes LSM mathematically very tractable because the Pythagorean theorem indicates that, when the error is independent of an estimated quantity, one can add the squared error and the squared estimated quantity. Third, themathematical tools and algorithms involved in LSM (derivatives, eigendecomposition, singular value decomposition) have been well studied for a relatively long time. LSM is one of the oldest techniques of modern statistics, and even though ancestors of LSM can be traced up to Greek mathematics, the first modern precursor is probably Galileo (see Harper, 1974, for a history and pre-history of LSM). The modern approach was first exposed in 1805 by the French mathematician Legendre in a now classic memoir, but this method is somewhat older because it turned out that, after the publication of Legendre’s memoir, Gauss (the famous German mathematician) contested Legen-
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تاریخ انتشار 2006