On Neyman–Pearson minimax detection of Poisson process intensity

M. V. Burnashev ()
Additional contact information
M. V. Burnashev: Russian Academy of Sciences

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 1, No 7, 221 pages

Abstract: Abstract The problem of the minimax testing of the Poisson process intensity $${\mathbf{s}}$$ s is considered. For a given intensity $${\mathbf{p}}$$ p and a set $$\mathcal{Q}$$ Q , the minimax testing of the simple hypothesis $$H_{0}: {\mathbf{s}} = {\mathbf{p}}$$ H 0 : s = p against the composite alternative $$H_{1}: {\mathbf{s}} = {\mathbf{q}},\,{\mathbf{q}} \in \mathcal{Q}$$ H 1 : s = q , q ∈ Q is investigated. The case, when the 1-st kind error probability $$\alpha $$ α is fixed and we are interested in the minimal possible 2-nd kind error probability $$\beta ({\mathbf{p}},\mathcal{Q})$$ β ( p , Q ) , is considered. What is the maximal set $$\mathcal{Q}$$ Q , which can be replaced by an intensity $${\mathbf{q}} \in \mathcal{Q}$$ q ∈ Q without any loss of testing performance? In the asymptotic case ( $$T\rightarrow \infty $$ T → ∞ ) that maximal set $$\mathcal{Q}$$ Q is described.

Keywords: Poisson process intensity; Error probabilities; Minimax testing of hypotheses (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s11203-020-09230-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:24:y:2021:i:1:d:10.1007_s11203-020-09230-4

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-020-09230-4

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().