Related papers: LqRT: Robust Hypothesis Testing of Location Parame…

The rapid development of LLMs has sparked extensive research into their factual knowledge. Current works find that LLMs fall short on questions around low-frequency entities. However, such proofs are unreliable since the questions can…

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…

The log-logistic distribution is a versatile parametric family widely used across various applied fields, including survival analysis, reliability engineering, and econometrics. When estimating parameters of the log-logistic distribution,…

We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can…

The Mann-Whitney-Wilcoxon rank sum test (MWWRST) is a widely used method for comparing two treatment groups in randomized control trials, particularly when dealing with highly skewed data. However, when applied to observational study data,…

Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…

In Change point detection task Likelihood Ratio Test (LRT) is sequentially applied in a sliding window procedure. Its high values indicate changes of parametric distribution in the data sequence. Correspondingly LRT values require…

Proportional hazards are a common assumption when designing confirmatory clinical trials in oncology. With the emergence of immunotherapy and novel targeted therapies, departure from the proportional hazard assumption is not rare in…

We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more…

A fundamental challenge in comparing two survival distributions with right censored data is the selection of an appropriate nonparametric test, as the power of standard tests like the Log rank and Wilcoxon is highly dependent on the often…

In this article, we propose a novel logistic quasi-maximum likelihood estimation (LQMLE) for general parametric time series models. Compared to the classical Gaussian QMLE and existing robust estimations, it enjoys many distinctive…

The parametric Welch $t$-test and the non-parametric Wilcoxon-Mann-Whitney test are the most commonly used two independent sample means tests. More recent testing approaches include the non-parametric, empirical likelihood and exponential…

We propose a new class of weighted logrank tests (WLRT) that control the risk of concluding that a new drug is more efficacious than standard of care, when, in fact, it is uniformly inferior. Perhaps surprisingly, this risk is not…

In practice, the logrank test is the most widely used method for testing the equality of survival distributions. It is the optimal method under the proportional hazard assumption. However, since non-proportional hazards are often…

In robust statistics, the breakdown point of an estimator is the percentage of outliers with which an estimator still generates reliable estimation. The upper bound of breakdown point is 50%, which means it is not possible to generate…

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use…

Non-proportional hazards (NPH) have been observed in confirmatory clinical trials with time to event outcomes. Under NPH, the hazard ratio does not stay constant over time and the log-rank test is no longer the most powerful test. The…

Testing the equality of two high-dimensional mean vectors is a fundamental problem in multivariate analysis. While the classical Hotelling's $T^2$ test is optimal in low-dimensional settings, it fails when the dimension $p$ is comparable to…

This paper derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a…