surerob: Robust estimation for Seemingly Unrelated Regression Models In robustsur: Robust Estimation for Seemingly Unrelated Regression Models

Description

Robust estimation for Seemingly Unrelated Regression Models in presence of cell-wise and case-wise outliers performed using a three-stage procedure. In the first step estimation of the coefficients in each single-equation model is obtained using a Robust Regression procedure, robust estimation of the residual covariance is obtained by a Two-Step Generalized S-estimator, a weighted least square is performed on the whole system to get final estimates of the regression coefficients.

Usage

 ```1 2 3``` ```surerob(formula, data, control=lmrob.control(), ...) ## S3 method for class 'surerob' print(x, digits=max(3, getOption("digits")-1), ...) ```

Arguments

 `formula` a list of objects of class `formula` for multiple-equation models; for single-equation models use function `lmrob`. `data` a list of objects of class `data.frame`. Each `data.frame` contains the data for the corresponding model and all the `data.frame`s must have the same number of observations. `control` list of control parameters. The default is constructed by the function `lmrob.control`, and it is passed to function `lmrob`. `...` arguments passed to the function `TSGS`. `x` an object of class `surerob`. `digits` number of digits to print.

Details

The estimation of systems of equations with unequal numbers of observations is not implemented.

Value

`surerob` returns a list of the class `surerob` and contains all results that belong to the whole system. This list contains one special object: "eq". It is a list and contains one object for each estimated equation. These objects are of the class `lmrob` and contain the results that belong only to the regarding equation.

The objects of the class `surerob` have the following components:

 `eq` a list that contains the results that belong to the individual equations. `call` the matched call. `method` estimation method. `rank` total number of linear independent coefficients. `coefficients` vector of all estimated coefficients. `fitted.values` matrix of fitted values. `residuals` matrix of residuals `imp.residuals` imputed residuals from `TSGS`. `residCovEst` residual covariance matrix used for estimation. `residCov` estimated residual covariance matrix. `rweights` matrix of robust weights. `TSGS` object from function `TSGS`. `control` list of control parameters used for the estimation. `df.residual` degrees of freedom of the whole system. `y` response observations used in the second step. `x` design matrix used in the second step.

Author(s)

Claudio Agostinelli and Giovanni Saraceno

References

Giovanni Saraceno, Fatemah Alqallaf and Claudio Agostinelli (2021?) A Robust Seemingly Unrelated Regressions For Row-Wise And Cell-Wise Contamination, submitted

`lmrob`, `lm` and `systemfit`
 ```1 2 3 4 5 6 7 8 9``` ``` library(systemfit) data("Kmenta") eqDemand <- consump~price+income eqSupply <- consump~price+farmPrice+trend system <- list(demand=eqDemand, supply=eqSupply) ## Robust estimation fitrob <- surerob(system, data=Kmenta) print(fitrob) ```