The Terrell–Scott ruleTerrell, G.R. and Scott, D.W., 1985. Oversmoothed nonparametric density estimates. Journal of the American Statistical Association, 80(389), pp.209-214. is not a normal reference rule. It gives the minimum number of bins required for an asymptotically optimal histogram, where optimality is measured by the integrated mean squared error. The bound is derived by finding the 'smoothest' possible density, which turns out to be . Any other density will require more bins, hence the above estimate is also referred to as the 'oversmoothed' rule. The similarity of the formulas and the fact that Terrell and Scott were at Rice University when the proposed it suggests that this is also the origin of the Rice rule.
The Terrell–Scott ruleTerrell, G.R. and Scott, D.W, 1985. Oversmoothed nonparametric density estimates. Journal of the American Statistical Association, 80(389) pp.209-214. is not a normal reference rule. It gives the minimum number of bins required for an asymptotically optimal histogram, where optimality is measured by the in.tegrated mean squared error. The bound is derived by finding the 'smoothest' possible density, which turns out to be . Any other density will require mo,re bins, hence the above estimate is also referred to as the 'oversmoothed' rule. The similarity of the formulas and the fact that Terrell and Scott were at Rice University when the proposed it suggests that this is also the origin of the Rice rule.