相关论文: The Likelihood Ratio Test in High-Dimensional Logi…
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…
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…
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the…
Consider $k$ independent random samples from $p$-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of $k$ covariance…
For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…
Wilk's theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that 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…
Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks' theorem. This assumption breaks down…
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…
In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an…
Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the…
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…
We explore the Wilks phenomena in two random graph models: the $\beta$-model and the Bradley-Terry model. For two increasing dimensional null hypotheses, including a specified null $H_0: \beta_i=\beta_i^0$ for $i=1,\ldots, r$ and a…
We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…
Likelihood ratio tests and the Wilks theorems have been pivotal in statistics but have rarely been explored in network models with an increasing dimension. We are concerned here with likelihood ratio tests in the $\beta$-model for…
We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…
We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…