Enforced continuity

In applied statistics, enforced continuity is a mathematical assumption rather than a statistical hypothesis in the classical piecewise regression analysis as well as the modern spline and smoothing methodology, with which an unknown threshold or knot can be estimated and the connection between two adjacent piecewise models can be ensured exactly. It was inaugurated by Sprent in 1961.

Inheritage

The assumption of enforced continuity was inherited by spline or smoothing techniques in the modern piecewise regression analysis in order to build up a smooth curve .

Theoretical problem and solution

A smooth curve looks like reasonable for a continuous random sample space in most situations, however in statistics, the enforced continuity assumption may arise a theoretical problem when treating a random sample space. What statistics should do is to build up a continuity test to infer whether the piecewise regression relationships are continuous at any unknown threshold in any situation, since any unknown threshold should be a random variable and the continuity of any two adjacent piecewise models should be randomly varibale, too. Therefore, we should need a continuity test before smoothing the connection of any two adiacent piecewise models . In contrary, we should have no confidence to smooth a connection if there were no the continuity test.

See also

• Spline
• Smoothing