Related papers: Wilks' theorems in the $\beta$-model
The complexity underlying real-world systems implies that standard statistical hypothesis testing methods may not be adequate for these peculiar applications. Specifically, we show that the likelihood-ratio test's null-distribution needs to…
This paper considers testing linear hypotheses of a set of mean vectors with unequal covariance matrices in large dimensional setting. The problem of testing the hypothesis $H_0 : \sum_{i=1}^q \beta_i \bmu_i =\bmu_0 $ for a given vector…
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…
This paper introduces a high-dimensional binary variate model that accommodates nonstationary covariates and factors, and studies their asymptotic theory. This framework encompasses scenarios where single indices are nonstationary or…
Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes…
Chatterjee, Diaconis and Sly (2011) recently established the consistency of the maximum likelihood estimate in the $\beta$-model when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we…
The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…
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…
A non parametric method based on the empirical likelihood is proposed for detecting the change in the coefficients of high-dimensional linear model where the number of model variables may increase as the sample size increases. This amounts…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FDEL) methodology for time series (on a regular grid), the formulation of…
An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…
This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and…
We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by…
This paper extends some prominent statistical results including \emph{Fisher Theorem and Wilks phenomenon} to the penalized maximum likelihood estimation with a quadratic penalization. It appears that sharp expansions for the penalized MLE…
A nonlinear model with response variable missing at random is studied. In order to improve the coverage accuracy, the empirical likelihood ratio (EL) method is considered. The asymptotic distribution of EL statistic and also of its…
This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is…
Motivated by the home-field advantage in sports, we propose a generalized Bradley--Terry model that incorporates covariate information for paired comparisons. It has an $n$-dimensional merit parameter $\bs{\beta}$ and a fixed-dimensional…
Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the $\beta$-model to weighted graphs. Similar to the $\beta$-model, each vertex in maximum entropy models is assigned a potential parameter,…
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…