The use of historical, i.e., already existing, estimates in current studies is common in a wide variety of application areas. Nevertheless, despite their routine use, the uncertainty associated with historical estimates is rarely properly accounted for in the analysis. In this communication, we review common practices and then provide a mathematical formulation and a principled frequentist methodology for addressing the problem of drawing inferences in the presence of historical estimates. Three distinct variants are investigated in detail; the corresponding limiting distributions are found and compared. The design of future studies, given historical data, is also explored and relations with a variety of other well-studied statistical problems discussed.
|Number of pages||34|
|Early online date||6 Jan 2023|
|State||E-pub ahead of print - 6 Jan 2023|
Bibliographical noteFunding Information:
Both authors thank COST Action IC1408 for Computationally Intensive Methods for the Robust Analysis of Non-standard Data that supported this research with grants for short visits. In addition the work of Ori Davidov was partially supported by the Israel Science Foundation Grants No. 456/17 and 2200/22 gratefully acknowledged. The authors are indebted to Anna Klimova for drawing their attention to the importance of Bliss independence and to the anonymous reviewers for their insightful and detailed comments.
© 2023, The Author(s).
- Loewner order
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty