Related papers: LqRT: Robust Hypothesis Testing of Location Parame…
Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional…
In this paper, we develop a generalization of the Gaussian quasi score test (GQST) for composite binary hypothesis testing. The proposed test, called measure transformed GQST (MT-GQST), is based on the score-function of the measure…
The density band model proposed by Kassam for robust hypothesis testing is revisited in this paper. First, a novel criterion for the general characterization of least favorable distributions is proposed, which unifies existing results. This…
This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…
The aim of this Lecture Note is to introduce the Signal Processing (SP) community to a powerful yet still under-utilised tool: the semiparametric statistics. In short, the semiparametric framework allows us to estimate or perform hypothesis…
We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…
We propose a testing procedure based on the Wilcoxon two-sample test statistic in order to test for change-points in the mean of long-range dependent data. We show that the corresponding self-normalized test statistic converges in…
This paper presents a hypothesis testing method given independent samples from a number of connected populations. The method is motivated by a forestry project for monitoring change in the strength of lumber. Traditional practice has been…
In this letter, the optimality of the likelihood ratio test (LRT) is investigated for binary hypothesis testing problems in the presence of a behavioral decision-maker. By utilizing prospect theory, a behavioral decision-maker is modeled to…
This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and…
Consider the likelihood ratio test (LRT) statistics for the independence of sub-vectors from a $p$-variate normal random vector. We are devoted to deriving the limiting distributions of the LRT statistics based on a random sample of size…
Despite the recent success of large language models (LLMs) in reasoning such as DeepSeek, we for the first time identify a key dilemma in reasoning robustness and generalization: significant performance degradation on novel or incomplete…
This note revisits Steel's multiple comparison test which uses Wilcoxon statistics in pairwise comparisons of several treatment samples with a common control sample. It derives means, variances and covariances of the Wilcoxon statistics…
We study a likelihood ratio test for detecting multiple {\it weak} changes in the mean of a class of CHARN models. The locally asymptotically normal (LAN) structure of the family of likelihoods under study is established. It results that…
Modern reinforcement learning (RL) can be categorized into online and offline variants. As a pivotal aspect of both online and offline RL, current research on the Bellman equation revolves primarily around optimization techniques and…
Prospect Theory (PT) models human decision-making behaviour under uncertainty, among which linguistic uncertainty is commonly adopted in real-world scenarios. Although recent studies have developed some frameworks to test PT parameters for…
This paper develops a unified framework for asymptotically minimax robust hypothesis testing under distributional uncertainty, applicable to both Bayesian and Neyman--Pearson formulations (Type-I and Type-II). Uncertainty classes based on…
Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…
Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…