相关论文: Q statistics in data depth: fundamental theory rev…
Dynamic treatment regimes (DTRs) have received an increasing interest in recent years. DTRs are sequences of treatment decision rules tailored to patient-level information. The main goal of the DTR study is to identify an optimal DTR, a…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids…
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile…
We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural…
A pair of variables that tend to rise and fall either together or in opposition are said to be monotonically associated. For certain phenomena, this tendency is causally restricted to a subpopulation, as, for example, an allergic reaction…
The compatibility of theoretically calculated values for the strong coupling constant,through the renormalization group approach with experimental data is studied. There exist considerable divergence in-between theoretical and experimental…
The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubic-rate estimators under the massive data framework. We develop a general theory for establishing…
Motivated by fast matrix multiplication and recent connections between asymptotic tensor rank and fine-grained complexity, we revisit classical tools from the matrix multiplication literature and develop a framework for obtaining improved…
Q-Learning is a fundamental off-policy reinforcement learning (RL) algorithm that has the objective of approximating action-value functions in order to learn optimal policies. Nonetheless, it has difficulties in reconciling bias with…
Case-cohort design, an outcome-dependent sampling design for censored survival data, is increasingly used in biomedical research. The development of asymptotic theory for a case-cohort design in the current literature primarily relies on…
Massive practical works addressed by Deep Q-network (DQN) algorithm have indicated that stochastic policy, despite its simplicity, is the most frequently used exploration approach. However, most existing stochastic exploration approaches…
In this study, we employ a superstatistical approach to construct q exponential and q Maxwell Boltzmann complex networks, generalizing the concept of scale free networks. By adjusting the crossover parameter {\lambda}, we control the degree…
A dynamic treatment regime effectively incorporates both accrued information and long-term effects of treatment from specially designed clinical trials. As these become more and more popular in conjunction with longitudinal data from…
The standard A/B testing approaches are mostly based on t-test in large scale industry applications. These standard approaches however suffers from low statistical power in business settings, due to nature of small sample-size or…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic…
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…