Related papers: Uniformly most powerful unbiased test for conditio…
In the multiple regression model we prove that the coefficient t-test for a variable of interest is uniformly most powerful unbiased, with the other parameters considered nuisance. The proof is based on the theory of tests with…
Gaussian Graphical Model selection problem is considered. Concentration graph is identified by multiple decision procedure based on individual tests. Optimal unbiased individual tests are constructed. It is shown that optimal tests are…
Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language,…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis…
This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…
In this paper, after a discussion of general properties of statistical tests, we present the construction of the most powerful hypothesis test for determining the existence of a new phenomenon in counting-type experiments where the observed…
The PC algorithm uses conditional independence tests for model selection in graphical modeling with acyclic directed graphs. In Gaussian models, tests of conditional independence are typically based on Pearson correlations, and…
Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…
We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…