Statistical Model

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data. It represents, often in considerably idealized form, the data-generating process. 
It is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory". 
All statistical hypothesis tests and all statistical estimators are derived via statistical models. They are part of the foundation of statistical inference.