Sequential Sampling Methods for Statistical Inference

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 July 2025 | Viewed by 2085

Special Issue Editors


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Guest Editor
Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
Interests: sequential analysis; sampling strategies; u-statistics; applications in agriculture; economics; environmental health and tourism

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Guest Editor
School of Informatics and Data Science, Hiroshima University, Hiroshima, Japan
Interests: survival analysis; copulas; competing risks; statistical decision theory; survival prognostic prediction; reliability; statistical process control; surrogate endpoints; meta-analysis; joint model

Special Issue Information

Dear Colleagues,

In many statistical inference problems where achieving a predetermined level of accuracy is desired, the absence of fixed-sample-size procedures presents a challenge, as the required sample size often depends on some unknown nuisance parameters. To solve such problems, sequential sampling has proved helpful.

A defining characteristic of sequential sampling is that the number of observations is determined as the experiment goes on, allowing for conclusions to be reached earlier. Because of such efficiency, sequential sampling methods are developed and implemented in various areas such as machine learning, data mining, environmental monitoring, quality control, clinical trials, and finance.

This Special Issue focuses on recent advances in sequential sampling methods for statistical inference. Potential topics of interest for submission include but are not limited to, sequential point and interval estimation, sequential hypothesis testing, change-point detection, and multi-armed bandits. We invite researchers from diverse backgrounds to contribute original articles that address the importance of sequential sampling methods and their role in statistical inference.     

Dr. Jun Hu
Prof. Dr. Takeshi Emura
Guest Editors

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Keywords

  • sequential sampling methods
  • statistical inference
  • point estimation
  • interval estimation
  • hypothesis testing
  • change-point detection
  • multi-armed bandits

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Published Papers (2 papers)

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14 pages, 317 KiB  
Article
Sequential Confidence Intervals for Comparing Two Proportions with Applications in A/B Testing
by Jun Hu, Lijia Zheng and Ibtihal Alanazi
Mathematics 2025, 13(1), 161; https://doi.org/10.3390/math13010161 - 5 Jan 2025
Viewed by 625
Abstract
This article addresses the use of fixed-width confidence intervals (FWCIs) for comparing two independent Bernoulli populations in A/B testing scenarios. Two sequential estimation procedures are proposed: one for estimating the difference in log probabilities of success and the other for log odds ratios. [...] Read more.
This article addresses the use of fixed-width confidence intervals (FWCIs) for comparing two independent Bernoulli populations in A/B testing scenarios. Two sequential estimation procedures are proposed: one for estimating the difference in log probabilities of success and the other for log odds ratios. Both methods showcase great efficiency, as established via theoretical analysis and Monte Carlo simulations. The practical utility of these methods is demonstrated through two real-world applications: analyzing retention rates in mobile game Cookie Cats and evaluating the effectiveness of online advertising. Full article
(This article belongs to the Special Issue Sequential Sampling Methods for Statistical Inference)
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16 pages, 571 KiB  
Article
Statistical Inference on the Shape Parameter of Inverse Generalized Weibull Distribution
by Yan Zhuang, Sudeep R. Bapat and Wenjie Wang
Mathematics 2024, 12(24), 3906; https://doi.org/10.3390/math12243906 - 11 Dec 2024
Viewed by 735
Abstract
In this paper, we propose statistical inference methodologies for estimating the shape parameter α of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for α and (2) a fixed-accuracy confidence interval estimation method for α [...] Read more.
In this paper, we propose statistical inference methodologies for estimating the shape parameter α of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for α and (2) a fixed-accuracy confidence interval estimation method for α. For (1), we introduce a purely sequential estimation strategy, which is theoretically shown to possess desirable first-order efficiency properties. For (2), we present a method that allows for the precise determination of sample size without requiring prior knowledge of the other two parameters of the IGW distribution. To validate the proposed methods, we conduct extensive simulation studies that demonstrate their effectiveness and consistency with the theoretical results. Additionally, real-world data applications are provided to further illustrate the practical applicability of the proposed procedures. Full article
(This article belongs to the Special Issue Sequential Sampling Methods for Statistical Inference)
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