基于凸对偶的复合假设检验

通过积分方程实现复合假设的一致相合比例估计：Gamma随机变量情形

Uniformly consistent proportion estimation for composite hypotheses via integral equations: "the case of Gamma random variables"

针对两类复合零假设的Gamma随机变量，提出基于Lebesgue-Stieltjes积分方程与调和分析的一致相合比例估计方法，无需p值，可用于高维模型稀疏度估计等场景。

Bayesian sequential composite hypothesis testing in discrete time

We study the sequential testing problem of two alternative hypotheses regarding an unknown parameter in an exponential family when observations are costly. In a Bayesian setting, the problem can be embedded in a Markovian framework. Using the conditional probability of one of the hypotheses as the underlying spatial variable, we show that the cost function is concave and that the posterior distribution becomes more concentrated as time goes on. Moreover, we study time monotonicity of the value function. For a large class of model specifications, the cost function is non-decreasing in time, and…

具有置信限的统计假设的序贯检验

Sequential Tests of Statistical Hypotheses with Confidence Limits

在本文中，我们提出了一个通用的方法来检验复合假设。我们的想法是使用置信限来定义停止和决策规则。通过调整置信限的系数，可以满足工作特征函数的要求。对于常见的分布，这种调整可以通过利用相关联的操作特征函数的单调性经由有效的计算来完成。我们发现，测试多个假设的问题，可以投到一般的框架，构建顺序随机区间与规定的覆盖概率。我们提出了一个包含原则构造多级测试计划。结果表明，我们提出的测试计划可以大大提高效率比顺序概率比测试及其变化。我们应用我们的一般方法来开发一个确切的方法来检验假设的差异，两个二项式比例。

A Generalized Frank-Wolfe Method With "Dual Averaging" for Strongly Convex Composite Optimization

We propose a simple variant of the generalized Frank-Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on the dual variables. We show that in this variant, one can choose a simple constant step-size and obtain a linear convergence rate on the duality gaps. By leveraging the convergence analysis of this variant, we then analyze the local convergence rate of the logistic fictitious play algorithm, which is well-established in game theory but lacks any form of convergence rate guarantees. We show that, with high probability, this…

An Asymptotic Theory of Joint Sequential Changepoint Detection and Identification for General Stochastic Models

The paper addresses a joint sequential changepoint detection and identification/isolation problem for a general stochastic model, assuming that the observed data may be dependent and non-identically distributed, the prior distribution of the change point is arbitrary, and the post-change hypotheses are composite. The developed detection-identification theory generalizes the changepoint detection theory developed by Tartakovsky (2019) to the case of multiple composite post-change hypotheses when one has not only to detect a change as quickly as possible but also to identify (or isolate) the tru…

关于复合假设的强p值和e值的存在性

On the existence of powerful p-values and e-values for composite hypotheses

针对复合零假设与备择假设为凸多面体时，证明当备择假设不与零假设生成空间相交时可构造满足分布要求的p值与e值，利用同时最优传输技术，首次刻画滤子粗化下的存在性并提供迭代构造方法。