*! version 1.0 03aug2015

Title

regmain -- Regression Specifying a Specific Error Term Distribution

Syntax

regmain
depvar
indepvars
[, options]

Main
distribution which distribution to use

initial initial values for the coefficients

nograph supresses the output of graphs

family allows you to compare all of the members in a distributio family. Either sgt or gb2.

maximize_options control the
maximization process

Description

regmain fits a model of depvar on indepvars using maximum likelihood with an error term distribution specified

Options

Main

distribution
SGT FAMILY: sgt, gt, st, sged, ged, t, normal, snormal, cauchy, scauchy, laplace, slaplace
GB2 FAMILY: gb2, gg, ln, lt, lcauchy, gamma, exp
Other: ols, lad, egb2, segb2

initial list of numbers that specifies the initial values of the coefficients.

nograph supresses the output of post estimation graphs.

family Select gb2 or sgt, cannot be used with distribution. This option will
run MLE regression with each distribution in the family and return a table of
log-likelihood values

maximize_options:
difficult,
technique(algorithm_spec),
iterate(#),
[no]log,
trace,
gradient,
showstep,
hessian,
showtolerance,
tolerance(#),
ltolerance(#),
nrtolerance(#); see [R] maximize.

Distributions

The following distributions or regression specifications can be used in the distribution option:

SGT Family

sgt Skewed Generalized T distribution (parameters: sigma lambda p q)

gt Generalized T distribution (parameters: sigma p q)

st Skewed T distribution (parameters: sigma lambda q)

sged Skewed Generalized Error Distribution (parameters: sigma lambda p)

ged Generalized Error Distribution (parameters: sigma p)

t T distribution (parameters: sigma q)

snormal Skewed Normal Distribution (parameters: sigma lambda )

normal Normal Distribution (parameters: sigma )

scauchy Skewed Cauchy Distribution (parameters: sigma lambda )

cauchy Cauchy Distribution (parameters: sigma )

slaplace Skewed Laplace Distribution (parameters: sigma lambda )

laplace LaplaceDistribution (parameters: sigma)

GB2 Family

gb2 Generalized Beta Distribution of the 2nd Kind (parameters: sigma p q)

gg Generalized Gamma Distribution(parameters: sigma p )

ln Log-Normal Distribution(parameters: sigma)

lt Log-T Distribution(parameters: sigma q)

lcauchy Log-Cauchy Distribution(parameters: sigma )

gamma Gamma Distribution(parameters: p )

exp Exponential Distribution(parameters: none )

Other options

ols Default, same as reg command

lad least absolute deviations, same as qreg command

egb2 exponential GB2 distribution(parameters: sigma delta p q)

segb2 Symmetric EGB2 distribution(parameters: sigma delta q)

Remarks

In cases where the convergence is difficult, try to use the option technique(bfgs), or the other technique options. technique(bfgs) is often more robust than the default technique(nr).

The default maximum number of iterations is 1000.

When specifying initial values, include values for estimation parameters as well as distributional parameters. The number of distributional parameters varies depending on which distribution is selected.

Examples

. clear

. set obs 1000

. set seed 1234

. gen x1 = rnormal(2,3)

. gen x2 = runiform(1,2)

. gen y = 1 + x1 + x2 + rt(5)

. regmain y x1 x2, dist(st) initial(1 1 1 3) nograph

Author

Authored by James McDonald and Jonathan Jensen at Brigham Young University. For
support contact Jonathan at jonathanjens@gmail.com.

References

Hansen, C., J. McDonald, and P. Theodossiou (2007) "Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models" Economics: The Open-Access, Open-Assessment E-Journal

McDonald J., R. Michelfelder, and P. Theodossiou (2010) "Robust Estimation with Flexible Parametric Distributions: Estimation of Utility Stock Betas" Quantitative Finance 375-387

McDonald, J.; Newey, W. (1998). "Partially Adaptive Estimation of Regression Models via the Generalized t Distribution". Econometric Theory. 4 (3): 428–457

McDonald, J.B. (1984) "Some generalized functions for the size distributions of income", Econometrica 52, 647–663.

Also see

https://en.wikipedia.org/wiki/Generalized_beta_distribution

https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution