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A Two-Step Test for the Two-Sample Problem of Processes of Ornstein-Uhlenbeck Type

Journal of Systems science & Complexity 2020年第6期33卷 2067-2079页

作者： WANG Yinfeng TANG Yanlin ZHANG Xinsheng School of Statistics and Mathematics Shanghai Lirin University of Acounting and FinanceShanghaiChina Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghaiChina Department of Statistics Fudan UniversityShanghaiChina

The authors propose a two-step test for the two-sample problem of processes of OrnsteinUhlenbeck type. In the first step, the authors test the equality of correlation structures, based on the least square estimators of the correlation parameters, and the test statistic follows the standard normal distribution. If the null hypothesis is not rejected in the first step, the authors consider a second step to test the equality of marginal distributions, based on the weighted deviation of the empirical characteristic functions;the test statistic has a complicated asymptotic distribution, so that sequential bootstrap method is applied to reach a temporary decision. Simulation studies and real data analysis suggest that the proposed approach performs well in finite samples.

关键词： Empirical characteristic functions hypothesis testing process of Ornstein-Uhlenbeck type sequential Bootstrap

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On the maximin distance properties of orthogonal designs via the rotation

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science China Mathematics 2023年第7期66卷 1593-1608页

作者： Yaping Wang Fasheng Sun Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of EducationSchool of StatisticsEast China Normal UniversityShanghai 200062China Key Laboratory for Applied Statistics of Ministry of Education School of Mathematics and StatisticsNortheast Normal UniversityChangchun 130024China

Space-filling designs are widely used in computer *** are frequently evaluated by the orthogonality and distance-related *** orthogonal arrays is an appealing approach to constructing orthogonal space-filling *** important issue that has been rarely addressed in the literature is the design selection for the initial orthogonal *** paper studies the maximin L_(2)-distance properties of orthogonal designs generated by rotating two-level orthogonal arrays under three *** provide theoretical justifications for the rotation method from a maximin distance perspective and further propose to select initial orthogonal arrays by the minimum G_(2)-aberration *** infinite families of orthogonal or 3-orthogonal U-type designs,which also perform well under the maximin distance criterion,are obtained and *** are presented to show the effectiveness of the constructed designs for building statistical surrogate models.

关键词： computer experiment Latin hypercube design minimum G_(2)-aberration space-filling design U-type design

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Semiparametric Likelihood-based Inference for Censored data with Auxiliary Information from External Massive data Sources

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Acta Mathematicae Applicatae Sinica 2020年第3期36卷 642-656页

作者： Yue-xin FANG Yong ZHOU School of Statistics and Management Shanghai University of Finance and EconomicsShanghai200433China Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOEand Academy of Statistics and Interdisciplinary SciencesEast China Normal UniversityShanghai 200062China

Published auxiliary information can be helpful in conducting statistical inference in a new *** this paper,we synthesize the auxiliary information with semiparametric likelihood-based inference for censoring data with the total sample size is *** express the auxiliary information as constraints on the regression coefficients and the covariate distribution,then use empirical likelihood method for general estimating equations to improve the efficiency of the interested parameters in the specified *** consistency and asymptotic normality of the resulting regression parameter estimators *** numerical simulation and application with different supposed conditions show that the proposed method yields a substantial gain in efficiency of the interested parameters.

关键词： Auxiliary information Massive data Censored data Empirical likelihood Estimation equations

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Unleashing the potential of prompt engineering for large language models

Patterns

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Patterns 2025年

作者： Chen, Banghao Zhang, Zhaofeng Langrené, Nicolas Zhu, Shengxin Advanced Institute of Natural Science Beijing Normal University No.18 Jingfeng Road Guangdong Zhuhai519087 China Guangdong Provincial/Zhuhai Key Laboratory of Interdisciplinary Research and Application for Data Science Beijing Normal-Hong Kong Baptist University Guangdong Zhuhai519087 China Department of Statistics and Data Science Beijing Normal-Hong Kong Baptist University Guangdong Zhuhai519087 China Department of Mathematical Science Beijing Normal-Hong Kong Baptist University Guangdong Zhuhai519087 China Department of Biomedical Informatics Yong Loo Lin School of Medicine National University of Singapore Singapore119228 Singapore Department of Mathematics University of Michigan Ann ArborMI48109 United States

This review explores the role of prompt engineering in unleashing the capabilities of large language models (LLMs). Prompt engineering is the process of structuring inputs, and it has emerged as a crucial technique for maximizing the utility and accuracy of these models. Both foundational and advanced prompt engineering methodologies—including techniques such as self-consistency, chain of thought, and generated knowledge, which can significantly enhance the performance of models—are explored in this paper. Additionally, the prompt methods for vision language models (VLMs) are examined in detail. Prompt methods are evaluated with subjective and objective metrics, ensuring a robust analysis of their efficacy. Critical to this discussion is the role of prompt engineering in artificial intelligence (AI) security, particularly in terms of defending against adversarial attacks that exploit vulnerabilities in LLMs. Strategies for minimizing these risks and improving the robustness of models are thoroughly reviewed. Finally, we provide a perspective for future research and applications. © 2025 The Author(s)

关键词： Visualization

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Simultaneous optimal control of directional missed discovery rates in data stream diagnosis

A I I E Transactions

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A I I E Transactions 2025年第4期57卷

作者： Yan He Yicheng Kang Dongdong Xiang Peihua Qiu a Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai China b Department of Information Systems & Analytics Miami University OxfordOH USA c Department of Biostatistics The University of Florida Gainsville FL USA

High-dimensional data streams are ubiquitous in modern manufacturing, due to their ability to provide valuable information about the industrial system’s performance on a real-time basis. If a shift occurs in a production process, fault diagnosis based on the data streams is of critical importance for identifying the root cause. Existing methods have largely focused on controlling the total missed discovery rate without distinguishing missed signals for positive versus negative components of the shift vector. In practice, however, losses incurred from the two directional shifts can differ substantially, so it is desirable to constrain the proportions of missed signals for positive and negative components at two distinctive levels. In this article, we propose a fault classification procedure that controls the two proportions separately. By formulating the problem as Lagrangian multiplier optimization, we show that the proposed procedure is optimal in the sense that it minimizes the expected number of false discoveries. We also suggest an iterative adjustment algorithm that converges to the optimal Lagrangian parameters. The asymptotic optimality for the data-driven version of our procedure is also established. Theoretical justification and numerical comparison with state-of-the-art methods show that the proposed procedure works well in applications.

关键词： Fault classification high-dimensional data large-scale testing Markov models post-signal diagnostics quality control

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Optimal mean-variance reinsurance and investment strategy with constraints in a non-Markovian regime-switching model

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Statistical theory and Related Fields 2020年第2期4卷 214-227页

作者： Liming Zhang Rongming Wang Jiaqin Wei Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghaiPeoples Republic of China

This paper is devoted to study the proportional reinsurance/new business and investment problem under the mean-variance criterion in a continuous-time *** strategies are constrained in the non-negative cone and all coefficients in the model except the interest rate are stochastic processes adapted the filtration generated by a Markov *** the help of a backward stochastic differential equation driven by the Markov chain,we obtain the optimal strategy and optimal cost explicitly under this non-Markovian regime-switching *** cases with one risky asset and Markov regime-switching model are considered as special cases.

关键词： Markov chain mean-variance problem non-negative constraints BSDE regime-switching

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A hybrid deep learning method for finite-horizon mean-field game problems

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Automatica 2025年 179卷

作者： Yu Zhang Zhuo Jin Jiaqin Wei George Yin Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai 200062 China Department of Actuarial Studies and Business Analytics Macquarie University 2109 NSW Australia Department of Mathematics University of Connecticut Storrs CT 06269-1009 USA

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in Markov chain approximation method and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved; two numerical examples are provided to illustrate the results.

关键词：

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A New Method for Computing the Expected Hitting Time between Arbitrary Different Configurations of the Multiple-Urn Ehrenfest Model

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数学研究 2022年第3期55卷 254-270页

作者： Sai Song Qiang Yao Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghai 200062China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghai 200062China NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai Shanghai 200062China

We study a multiple-urn version of the Ehrenfest *** this setting,we denote the n urns by Urn l to Urn n,where n≥***,M balls are randomly placed in the n *** each subsequent step,a ball is selected and put into the other n-1 urns with equal *** expected hitting time leading to a change of the M balls'status is computed using the method of stopping *** a corollary,we obtain the expected hitting time of moving all the M balls from Urn 1 to Urn 2.

关键词： Ehrenfest urn model Markov chain random walk hitting time

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Estimation of Scale Transformation for Approximate Periodic Time Series with Long-Term Trend

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Journal of Mathematical Research with applications 2021年第3期41卷 238-258页

作者： Shujin WU Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics Faculty of Economics and Management East China Normal University

Approximate periodic time series means it has an approximate periodic trend. The so-called approximate periodicity refers that it looks like having periodicity, however the length of each period is not constant such as sunspot data. Approximate periodic time series has a wide application prospect in modelling social economic phenomenon. As for approximate periodic time series, the key problem is to depict its approximate periodic trend because it can be dealt as an ordinary time series only if its approximate periodic trend has been depicted. However,there is little study on depicting approximate periodic *** the paper, the authors first establish some necessary theories, especially bring forward the concept of shape-retention transformation with lengthwise compression and obtain necessary and sufficient condition for linear shape-retention transformation with lengthwise compression,then basing on the theories the authors present a method to estimate scale transformation, which can model approximate periodic trend very clearly. At last, a simulated example is analyzed by this presented method. The results show that the presented method is very effective and very powerful.

关键词： time series approximate periodicity scale transformation shape-retention transformation with lengthwise compression

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Analysis of Stock Splits Based on Risk theory: Empirical Evidence from the Chinese Stock Markets

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Journal of Systems science and Information 2022年第1期10卷 19-34页

作者： Shujin WU Tong XU MOE Key Laboratory of Advanced Theory and Application in Statistics and Data Science School of StatisticsEast China Normal UniversityShanghai 200062China School of Statistics East China Normal UniversityShanghai 200062China

The paper first analyzes price change due to stock splits in Chinese stock markets,which shows stock prices typically go up for stock *** theoretical analyses based on risk theory are presented to explain the reason,where the method comes from a new perspective and obtained theoretical conclusions show that stock splits typically make stock price go up if risk-compensation function is convex,and go down if risk-compensation function is *** prices typically go up for stock splits because risk-compensation functions are mainly *** obtained conclusions are consistent with the known results in the last three decades.

关键词： stock split risk theory price Chinese stock markets

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