Related papers: U-Statistics Based Jackknife Empirical Likelihood …
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…
We propose new classes of tests for the Pareto type I distribution using the empirical characteristic function. These tests are $U$ and $V$ statistics based on a characterisation of the Pareto distribution involving the distribution of the…
The likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks' theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the…
Linear mixed-effects models are widely used in analyzing repeated measures data, including clustered and longitudinal data, where inferences of both fixed effects and variance components are of importance. Unlike the fixed effect inference…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
We consider the hypothesis testing problem that two vertices $i$ and $j$ of a generalized random dot product graph have the same latent positions, possibly up to scaling. Special cases of this hypothesis test include testing whether two…
Jackknife empirical likelihood (JEL) is an effective modified version of empirical likelihood method (EL). Through the construction of the jackknife pseudo-values, JEL overcomes the computational difficulty of EL method when its constraints…
Confidence curves are used in uncertainty validation to assess how large uncertainties ($u_{E}$) are associated with large errors ($E$). An oracle curve is commonly used as reference to estimate the quality of the tested datasets. The…
Inequality (concentration) curves such as Lorenz, Bonferroni, Zenga curves, as well as a new inequality curve -- the $D$ curve, are broadly used to analyse inequalities in wealth and income distribution in certain populations. Quantile…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
Two-sample hypothesis testing for large graphs is popular in cognitive science, probabilistic machine learning and artificial intelligence. While numerous methods have been proposed in the literature to address this problem, less attention…
In this paper, we construct a consistent non-parametric test for testing the equality of population medians for different samples when the observations in each sample are independent and identically distributed. This test can be further…
We prove ratio-consistency of the jackknife variance estimator, and certain variants, for a broad class of generalized U-statistics whose variance is asymptotically dominated by their H\'ajek projection, with the classical fixed-order case…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…