Local asymptotic coding and the minimum description length

Local asymptotic arguments imply that parameter selection via the minimum d escription length (MDL) resembles a traditional hypothesis test, A common a pproximation for MDL estimates the cost of adding a parameter at about (1/2 )log n bits for a model fit to n observations, While accurate for parameter s which are large on a standardized scale, this approximation overstates th e parameter cost near zero, We find that encoding the parameter produces a shorter description length when the corresponding estimator is about two st andard errors away from zero, as in a traditional statistical hypothesis te st.