estat
The estat command calculated scalar and matrix based statistics. The precise capabilities of
estat depend on what command you run before it. There are three types that are available after any estimation command. For specific forms of estat available after a command, try typing help [command] postestimation For example. help regress postestimation or see the corresponding entry in [R]. The three postestimations performed by estat following any estimation are estat ic estat summarize and estat vce are are the focus of the below.
The estat ic command calculates two information criteria (ic) which can be used to compare the fit of different models. It can be used after any command which includes a report of log likelihood. The first criterion computed is the AIC short for Akaike Information Criterion. A basic introduction and links to useful resources can be found on Wikipedia. The second information criterion computed is the BIC or Bayesian Information Criterion. A basic introduction and links to useful resources can be found on Wikipedia. These two criteria are not always in agreement about which model is a better fit.
The estat summarize command shows summary staistics (mean, std. deviation, min, and max) for all variables involved in the model. Additionally, you can specify ,labels to display variable labels
noheader to suppress the table header noweights to ignore weights from a previous estimation command and equation which displays repeat summary statistics multiple times for variables involved in multiple rquations.
The estat vce command calculates the variance-covariance matrix of the parameters of the model used in the estimation command. A fairly basic intro to covariance matrices can be found here. Another basic introduction can be found at the government's NIST Statistics for Engineering page. A good explanation/example of variance and covariance can also be found from the Visual Statistics website.