What is this type of data called? An event occurs once per period, such as once per year. Time is measured in discrete units, such as days of the year. Let $A_y$ be the day in year $y$ on which this event occurs. However, we do not observe $A_y$. Instead, in each period, we observe the following two days: $L_y$, a day that occurs some time before $A_y$ ($L_y < A_y$); and $E_y$, a day on which we know that the event has already occurred ($E_y \ge A_y$).
What is this type of data called?
Are there papers that deal with this data and develop an estimator for $A$?

I believe this is interval censoring.

"In statistical literature, interval censoring usually represents a sampling scheme or an incomplete data structure. By interval censoring, we mean that a random variable of interest is known only to lie within an interval instead of being observed exactly. For applications in survival analysis, the random variable is the time to some event such as death, a disease recurrence or a distant metastasis."

Zhang Z, Sun J. Interval censoring. Stat Methods Med Res. 2010 Feb;19(1):53-70. doi: 10.1177/0962280209105023. Epub 2009 Aug 4. PMID: 19654168; PMCID: PMC3684949.
