Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based on minimizing the sum of absolute deviations (also sum of absolute residuals or sum of absolute errors) or the L1 norm of such values. It is analogous to the least squares technique, except that it is based on absolute values instead of squared values. It attempts to find a function which closely approximates a set of data by minimizing residuals between points generated by the function and corresponding data points. The LAD estimate also arises as the maximum likelihood estimate if the errors have a Laplace distribution. It was introduced in 1757 by Roger Joseph Boscovich.[1]
^"Least Absolute Deviation Regression". The Concise Encyclopedia of Statistics. Springer. 2008. pp. 299–302. doi:10.1007/978-0-387-32833-1_225. ISBN 9780387328331.
and 26 Related for: Least absolute deviations information
Leastabsolutedeviations (LAD), also known as leastabsolute errors (LAE), leastabsolute residuals (LAR), or leastabsolute values (LAV), is a statistical...
The average absolutedeviation (AAD) of a data set is the average of the absolutedeviations from a central point. It is a summary statistic of statistical...
of 2. The absolutedeviations about 2 are (1, 1, 0, 0, 2, 4, 7) which in turn have a median value of 1 (because the sorted absolutedeviations are (0, 0...
some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares cost function as in ridge regression...
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting...
that are less sensitive to outliers than the least squares estimates, is to use leastabsolutedeviations. Even then, gross outliers can still have a considerable...
proportional to the absolute value function, and thus median regression is the same as linear regression by leastabsolutedeviations. The mathematical...
Partial least squares regression (PLS regression) is a statistical method that bears some relation to principal components regression; instead of finding...
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model. It is used when there...
that can be used in place of ordinary least squares include leastabsolutedeviations (minimizing the sum of absolute values of residuals) and the Theil–Sen...
{\displaystyle E(Y_{i}|X_{i})} . However, alternative variants (e.g., leastabsolutedeviations or quantile regression) are useful when researchers want to model...
doi:10.1016/0315-0860(74)90033-0. Smith, Kirstine (1918). "On the Standard Deviations of Adjusted and Interpolated Values of an Observed Polynomial Function...
this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the...
Ridge regression was developed as a possible solution to the imprecision of least square estimators when linear regression models have some multicollinear...
Weighted least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge...
minimizes expected absolute error. Leastabsolutedeviations shares the ability to be relatively insensitive to large deviations in outlying observations...
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems...
N} is the total number of observations. G-tests have been recommended at least since the 1981 edition of the popular statistics textbook by Robert R. Sokal...
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model...
}}^{(t)}{\big |}^{p-2}.} In the case p = 1, this corresponds to leastabsolutedeviation regression (in this case, the problem would be better approached...
standard deviations for β {\displaystyle \mathbf {\beta } } and α i {\displaystyle \alpha _{i}} can be determined via classical ordinary least squares...
In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational...
{\mu }}|.} revealing a link between the Laplace distribution and leastabsolutedeviations. A correction for small samples can be applied as follows: b ^...
emergency, by Specific Area Message Encoding Leastabsolute errors, an alternate name for leastabsolutedeviations in statistics Loterías y Apuestas del Estado...
Global Information