Robust and Deterministic Linear Regression via DetLTS
Description
Function to compute the DetLTS estimates of regression.
Usage
1 
Arguments
x 
Matrix of design variables. Never contains an intercept. 
y 
Vector of responses. 
intercept 
A boolean indicating whether the regression contains an intercept. 
alpha 
numeric parameter controlling the size of the subsets over which the determinant is minimized, i.e., alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.75. Can be a vector. 
h 
Integer in [ 
scale_est 
A character string specifying the variance functional. Possible values are "Qn" or "scaleTau2". 
Value
The function DetLTS
returns a list with as many components as
there are elements in the h
. Each of the entries is a list
containing the following components:
crit 
the value of the objective function of the LTS regression method, i.e., the sum of the h smallest squared raw residuals. 
coefficients 
vector of coefficient estimates (including the intercept by default when

best 
the best subset found and used for computing the raw estimates, with

fitted.values 
vector like 
residuals 
vector like 
scale 
scale estimate of the reweighted residuals. 
alpha 
same as the input parameter 
quan 
the number h of observations which have determined the least trimmed squares estimator. 
intercept 
same as the input parameter 
cnp2 
a vector of length two containing the consistency correction factor and the finite sample correction factor of the final estimate of the error scale. 
raw.coefficients 
vector of raw coefficient estimates (including
the intercept, when 
raw.scale 
scale estimate of the raw residuals. 
raw.resid 
vector like 
raw.cnp2 
a vector of length two containing the consistency correction factor and the finite sample correction factor of the raw estimate of the error scale. 
lts.wt 
vector like y containing weights that can be used in a weighted least squares. These weights are 1 for points with reasonably small residuals, and 0 for points with large residuals. 
raw.weights 
vector containing the raw weights based on the raw residuals and raw scale. 
method 
character string naming the method (Least Trimmed Squares). 
Author(s)
Vakili Kaveh using translation of the C code from pcaPP (by Peter Filzmoser, Heinrich Fritz, Klaudius Kalcher, see citation("pcaPP")) for the Qn and scaleTau2 (Original by Kjell Konis with substantial modifications by Martin Maechler) from robustbase (see citation("scaleTau2")) as well as R code from function ltsReg in package robustbase (originally written by Valentin Todorov valentin.todorov@chello.at, based on work written for Splus by Peter Rousseeuw and Katrien van Driessen from University of Antwerp, see citation("ltsReg")).
References
Vakili K. (2016). A study and implementation of robust estimators for multivariate and functional data (Doctoral dissertation).
Maronna, R.A. and Zamar, R.H. (2002) Robust estimates of location and dispersion of highdimensional datasets; Technometrics 44(4), 307–317.
Rousseeuw, P.J. and Croux, C. (1993) Alternatives to the Median Absolute Deviation; Journal of the American Statistical Association , 88(424), 1273–1283.
Peter J. Rousseeuw (1984), Least Median of Squares Regression. Journal of the American Statistical Association 79, 871–881.
P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.
P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212–223.
Pison, G., Van Aelst, S., and Willems, G. (2002) Small Sample Corrections for LTS and MCD. Metrika 55, 111123.
Examples
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