First declaration time

Read the equation

The infimum selects the earliest time at which the declaration indicator is one. On a discrete record it is simply the first qualifying sample index. If the qualifying set is empty, the event is unobserved and requires an explicit missing or censoring convention.

Terms & definitions

How it works

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Original context

2.2 Declaration, onset, and persistence

Once a declaration detector has been specified independently, define

tD=inf{t:Dt=1}.

For a selected discrepancy and tolerance ε, a finite-horizon candidate onset is

tHW=inf{t>tD:δt+k>ε for k=0,…,W−1}.

This is a retrospective event time: at t one does not yet know whether the next W−1 observations will satisfy the condition. An online detector must wait for the required window and report that detection delay.

{t}_{D}=inf{t:{D}_{t}=1}.