Related papers: Q statistics in data depth: fundamental theory rev…

For the multi-sample equal covariance function (ECF) testing problem, Zhang (2013) proposed an $L^{2}$-norm based test. However, its asymptotic power and finite sample performance have not been studied. In this paper, its asymptotic power…

This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…

We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…

This paper analyzes over 30 types of q-series and the asymptotic behavior of their expansions. A method is described for deriving further asymptotic formulas using convolutions of generating functions with subexponential growth. All…

Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…

We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to…

Diffusion models excel at generating high-likelihood samples but often require alignment with downstream objectives. Existing fine-tuning methods for diffusion models significantly suffer from reward over-optimization, resulting in…

Despite the great empirical success of deep reinforcement learning, its theoretical foundation is less well understood. In this work, we make the first attempt to theoretically understand the deep Q-network (DQN) algorithm (Mnih et al.,…

Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a…

Database theory is exciting because it studies highly general and practically useful abstractions. Conjunctive query (CQ) evaluation is a prime example: it simultaneously generalizes graph pattern matching, constraint satisfaction, and…

The compensated quotient-difference (Compqd) algorithm is proposed along with some applications. The main motivation is based on the fact that the standard quotient-difference (qd) algorithm can be numerically unstable. The Compqd algorithm…

We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…

The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar non-equilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained…

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…

Reinforcement learning (RL) has emerged as a key approach for training agents in complex and uncertain environments. Incorporating statistical inference in RL algorithms is essential for understanding and managing uncertainty in model…

Starting with Tukey's pioneering work in the 1970's, the notion of depth in statistics has been widely extended especially in the last decade. These extensions include high dimensional data, functional data, and manifold-valued data. In…

The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…

We consider a reinforcement learning setting in which the deployment environment is different from the training environment. Applying a robust Markov decision processes formulation, we extend the distributionally robust $Q$-learning…

A number of popular estimators of the between-study variance, $\tau^2$, are based on the Cochran's $Q$ statistic for testing heterogeneity in meta analysis. We introduce new point and interval estimators of $\tau^2$ for log-odds-ratio.…

We revisit the classical broken sample problem: Two samples of i.i.d. data points $\mathbf{X}=\{X_1,\cdots, X_n\}$ and $\mathbf{Y}=\{Y_1,\cdots,Y_m\}$ are observed without correspondence with $m\leq n$. Under the null hypothesis,…