Stat Colloquium: Dr. Jing Li
UMBC
Location
Mathematics/Psychology : 401
Date & Time
October 25, 2024, 11:00 am – 12:00 pm
Description
Title: Multi-Stage Sampling Strategies for MRPE Problems with an Unknown Scale Parameter in a Gamma Population
Abstract:
In this talk, I will present a general multi-stage sampling strategy to address
MRPE (Minimum Risk Point Estimation) problems for a function g(β) involving an
unknown scale parameter within a Gamma population, assuming the shape parameter
α (where α>0) is known. We approach the problem under the SEL (Squared Error
Loss) framework, incorporating sampling costs. First, I will outline a
foundational theoretical structure, derived under general conditions on g(β)
and additional sufficient conditions for the multi-stage strategy itself. I
will also discuss the asymptotic first-order efficiency of the proposed MRPE
strategy, which our paper demonstrates (Theorem 4.1) to meet the asymptotic
risk efficiency criteria. Furthermore, I will introduce purely sequential,
accelerated sequential, and three-stage estimation strategies, each of which
achieves both first-order and asymptotic risk efficiency under general
conditions. The talk will also include extensive data analysis from
simulations, along with illustrative application using a bone marrow transplant
(BMT) dataset. Lastly, I will present potential extensions of the MRPE
framework, including sampling strategies for analogous problems under
mixture-gamma distributions, demonstrating how these strategies fit into the
broader context of related statistical challenges.
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