ltsReg {rrcov} R Documentation

## Robust regression with high breakdown point

### Description

Carries out least trimmed squares (LTS) regression.

### Usage

```ltsReg(x, y, intercept=TRUE, alpha=NULL, nsamp=500, adjust=FALSE, mcd=TRUE, qr.out=FALSE, yname=NULL, seed=0)
```

### Arguments

 `x` a matrix or data frame containing the explanatory variables. `y` the response: a vector of length the number of rows of 'x'. `intercept` if true, a model with constant term will be itted; otherwise no constant term will be included. Default is `intercept = TRUE` `alpha` the percentage of squared residuals whose sum will be minimized. Its default value is 0.5. In general, alpha must be a value between 0.5 and 1. `nsamp` number of subsets used for initial estimates. Default is `nsamp = 500` `adjust` whether to perform intercept adjustment at each step. This could be quite time consuming, therefore the default is `adjust = FALSE` `mcd` whether to compute robust distances using Fast-MCD. `qr.out` whether to return the QR decomposition. Default is `qr.out = FALSE` `yname` the name of the dependent variable. Default is `yname = NULL` `seed` starting value for random generator. Default is `seed = 0`

### Details

The LTS regression method minimizes the sum of the h smallest squared residuals, where h must be at least half the number of observations. The default value of h is roughly 0.5n where n is the total number of observations, but the user may choose any value between n/2 and n. The computations are performed using the Fast LTS algorithm proposed by Rousseeuw and Van Driessen (1999).

### Value

An object of class '"lts"'. This is a list with 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,when intercept=TRUE), obtained after reweighting `best` the best subset found and used for computing the raw estimates. The size of `best` is equal to `quan`. `fitted.values` vector like y containing the fitted values of the response after reweighting. `residuals` vector like y containing the residuals from the weighted least squares regression. `scale` scale estimate of the reweighted residuals. `rsquared` robust version of R squared. `alpha` same as the input parameter `alpha`. `quan` the number h of observations that have determined the least trimmed squares estimator `intercept` same as the input parameter `intercept`. `raw.coefficients` vector of raw coefficient estimates (including the intercept,when intercept=TRUE). `raw.scale` scale estimate of the raw residuals. `raw.resid` vector like y containing the raw residuals from the regression. `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 raw residuals, and 0 for points with large raw residuals. `method` character string naming the method (Least Trimmed Squares). `X` the input data as a matrix.

### References

p. j. Rousseeuw (1984), Least Median of Squares Regression. Journal of the American Statistical Association, 79, pp. 871-881.

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.

P. J. Rousseeuw and K. van Driessen (1999) Computing LTS Regression for Large Data Sets, Technical Report, University of Antwerp, submitted

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, 111-123.

`covMcd`
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