Estimating Robust Regression in EViews

To estimate an equation using robust regression, open the equation dialog by selecting Quick/Estimate Equation…, or by selecting Object/New Object…/Equation and selecting ROBUSTLS from the Method dropdown menu. EViews will display the robust regression dialog:

The Specification tab lets you enter the basic regression specification and the type of robust regression to be performed:

• Enter the regression specification in list form (dependent variable followed by the list of regressors) in the Equation specification variable edit field.

• Specify the estimation type by choosing one of the three estimation types M‑estimation, S-estimation, or MM-estimation in the Robust estimation type dropdown. By default, EViews will perform M‑estimation.

• Enter the estimation Sample in the edit field

Click on OK to estimate the equation using the default settings, or click on Options to inspect settings for advanced options.

Options

Clicking on the Options tab of the dialog lets you specify advanced estimation options. The tab will display different settings depending on whether you choose M-estimation, S-estimation, or MM-estimation in the Robust estimation type dropdown.

M-estimation options

For M-estimation, you will be offered choices the for objective specification, scale estimator, and covariance type.

Objective specification

The Objective specification section of the dialog controls the choice of function and the tuning constant:

• You should use the Function dropdown to choose from among the 10 available functions: Andrews, Bisquare, Cauchy, Fair, Huber, Huber-Bisquare, Logistic, Median, Talworth, and Welsch (Bisquare is the default).

• The Scale using H-matrix checkbox may be used to define individual weights as described in Equation (31.4).

• The Default constant and User-specified constant radio buttons should be used to specify the value of the tuning constant. Choosing Default constant will use the Holland and Welsch (1977) values of the tuning constant as described on page 1278. To provide your own tuning value, select User-specified constant and enter a positive number or name of a scalar object in the Tuning value edit field.

Scale estimates

The Scale estimates dropdown is used to select between Mean Absolute Deviation (MAD) with either zero or median centering, Huber scaling, or a user-specified scale. The default estimator is MAD with median centering. To provide a user-specified scale, select Fixed user in the dropdown and enter a positive number or name of a scalar object in the User scale edit field

Other settings

The Covariance type dropdown allows you to choose between the three types of Huber covariance methods.

The Iteration control section controls the maximum iterations and convergence tolerances used when solving the nonlinear equations in Equation (31.5). Click on Display Settings to show information in the EViews output.

You may use the Coefficient name edit field to specify a coefficient vector other than the default C to hold the results from estimation.

S-estimation options

The S-estimator offers a set of estimation options than differs markedly from those offered by the M-estimator. In contrast to the M-estimator, there is no option for choosing the scale estimator. You will, however, be offered a slightly modified set of Objective specification options and a new set of S options.

Objective specification

The Objective specification section of the dialog allows you to specify the values of the tuning and breakdown constants:

• You should select Default constant to use the default value of 1.5476 (0.5 breakdown) or you may select User-specified constant and enter a value or name of a scalar in the Tuning value edit field. The tuning value must be positive.

• Note that the function choice dropdown is disabled since the S-estimation function is restricted to be the Tukey Bisquare.

S settings

The S options portion of the dialog allows you to control the settings for the Fast-S algorithm:

• Number of trials controls the number of S subsample estimates to be computed. By default, EViews will compute 200 estimates.

• Initial sample size specifies the size of each random subsample used in the S initializing regression. By default, this field will be initialized at the number of regressors.

• Max refinements controls the number of refinements to each initial subsample regression estimate. Each refinement consists of a single modified M-estimator step toward the solution of the nonlinear equations.

• Number of comparisons is the number of best estimates that are candidates for refinement and comparison to find the final estimate.

• The Random generator and Seed fields control the construction of the random subsamples required for the Fast-S algorithm. You may the leave the Seed field blank, in which case EViews will use the clock to obtain a seed at the time of estimation, or you may provide an integer from 0 to 2,147,483,647. The Clear button may be used to clear the seed used by a previously estimated equation.

For additional discussion of these settings, see “S-estimator calculation”.

Other settings

The Coefficient name, Covariance type, and Iteration control settings are as described in “M-estimation options”.

MM-estimation options

The options for the MM-estimator are closely related to the options for the S-estimator described in “S-estimation options”.

The main difference between the MM and S options is in the settings for the tuning parameters. Since the MM estimator combines both S and M estimation, the dialog has separate fields for the tuning values used in the S-estimation and the tuning value used in the M-estimation.

The Default constants setting sets an S tuning parameter of 1.5476 (0.5 breakdown) and a default M tuning value of 4.684 (for 0.95 relative efficiency under normal errors).