Related papers: Likelihood ratio tests under model misspecificatio…
The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix…
Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…
This paper deals with the local asymptotic structure, in the sense of Le Cam's asymptotic theory of statistical experiments, of the signal detection problem in high dimension. More precisely, we consider the problem of testing the null…
Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Oftentimes, the number of observations is small, and it is thus important to…
To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests…
Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent…
This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate…
This paper is to prove the asymptotic normality of a statistic for detecting the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size $n$ tends to infinity and the…
Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model…
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…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
In the high dimensional Stochastic Blockmodel for a random network, the number of clusters (or blocks) K grows with the number of nodes N. Two previous studies have examined the statistical estimation performance of spectral clustering and…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
In this paper, we consider the problem of testing equality of the covariance matrices of L complex Gaussian multivariate time series of dimension $M$ . We study the special case where each of the L covariance matrices is modeled as a rank K…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
Impropriety testing for complex-valued vector has been considered lately due to potential applications ranging from digital communications to complex media imaging. This paper provides new results for such tests in the asymptotic regime,…
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…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…