Admissible and Minimax Estimation of the Parameters of the Selected Normal Population in Two-Stage Adaptive Designs Under Reflected Normal Loss Function

• Autorzy: Mazarei Hasan , Nematollahi Nader

Identyfikatory

DOI

10.19195/0208-4147.39.2.7

• Języki publikacji: EN

Abstrakty

EN

In clinical research, one of the key problems is to estimate the effect of the best treatment among the given k treatments in two-stage adaptive design. Suppose the effects of two treatments have normal distributions with means θ₁ and θ₂, respectively, and common known variance σ². In the first stage, random samples of size n₁ with means X₁ and X₂ are chosen from the two populations. Then the population with the larger (or smaller) sample mean X_M is selected, and a random sample of size n₂ with mean Y_M is chosen from this population in the second stage of design. Our aim is to estimate the mean θ_M (or θ_J) of the selected population based on X_M and Y_M in two-stage adaptive design under the reflected normal loss function. We obtain minimax estimators of θ_M and θ_J, and then provide some sufficient conditions for the inadmissibility of estimators of θ_M and θ_J. Theoretical results are augmented with a simulation study as well as a real data application.

Słowa kluczowe

EN

inadmissible estimator; minimax estimator; reflected normal loss function; two-stage adaptive design

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 361--383
• Opis fizyczny: Bibliogr. 36 poz., tab., wykr.

Twórcy

autor

Mazarei Hasan

• Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

autor

Nematollahi Nader

• Department of Statistics, Allameh Tabataba’i University, Tehran, Iran

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).