Empirical estimation of d-risks at distinguishing one-sided hypotheses
- Авторлар: Simushkin D.1
-
Мекемелер:
- Department of Mathematical Statistics
- Шығарылым: Том 37, № 4 (2016)
- Беттер: 509-514
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198190
- DOI: https://doi.org/10.1134/S199508021604017X
- ID: 198190
Дәйексөз келтіру
Аннотация
This paper deals with problem of distinguishing between the two hypotheses H0: θ ≤ 0, H1: θ > 0 based on a fixed volume sample with a normal distribution N(θ, 1), θ ∈ R. It is considered by suppose that the true value θ is a realization of a random value ϑ with some unknown a priori density g(θ). An empirical estimate g(θ) based on the estimate of archive data of prior distribution characteristic function is suggested for the d-risk of the optimal criteria (conditional probability of justice of hypothesis Hj in condition that it is rejected, j = 0, 1). Consistency of empirical estimators of d-risks and appropriate critical values are studied. The rate of convergence is discovered from obtained estimates.
Негізгі сөздер
Авторлар туралы
D. Simushkin
Department of Mathematical Statistics
Хат алмасуға жауапты Автор.
Email: simdim555@gmail.com
Ресей, Kremlevskaya ul. 35, Kazan, Tatarstan, 420008