People use RMSE to validate Vasicek model. But I am not sure how to calculate it because RMSE = std deviation ( original yield - forecasted yield) and forecasted yield can have multiple values because it depends on r(t) and r(t) has a random term.Any guidelines on how to calculate it will be really helpful. Any link to a research paper or online resource will be appreciated

There are many ways to attempt to validate/test a yield curve model. Looking at its ability to forecast the level of yields does not seem very interesting, since we know a priori that standard term structure models are pretty much useless in this task. Three main approaches to test the (classic) Vasicek model would be:1. Cross-sectional restrictions on yields, i.e. curve shape. The model tells you exactly what all yields should be as a function of three parameters + the short rate. Find the set of parameters that minimize the difference between model yields and market yields.2. Restrictions on yield moves. Easiest to check in forward rate space, at the cost of adding some noise from your curve fitting. The model tells you that there should be a single principal component driving the forward curve moves, and that this should be exponentially declining as a function of maturity.3. Restrictions on option pricing. The model prescribes the value of options (e.g. swaptions, caps/floors, Eurodollar futures options, ...) relative to the underlying curve.