Related papers: Inference for Large-Scale Linear Systems with Know…

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…

This paper proposes a new approach to obtain uniformly valid inference for linear functionals or scalar subvectors of a partially identified parameter defined by linear moment inequalities. The procedure amounts to bootstrapping the value…

This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…

In this paper, we study a generalization of the two-groups model in the presence of covariates --- a problem that has recently received much attention in the statistical literature due to its applicability in multiple hypotheses testing…

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…

The fields of quantum non-locality in physics, and causal discovery in machine learning, both face the problem of deciding whether observed data is compatible with a presumed causal relationship between the variables (for example a local…

This paper addresses patient heterogeneity associated with prediction problems in biomedical applications. We propose a systematic hypothesis testing approach to determine the existence of patient subgroup structure and the number of…

Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…

We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…

This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of…

We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…

System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…

In analyzing high-dimensional models, sparsity of the model parameter is a common but often undesirable assumption. In this paper, we study the following two-sample testing problem: given two samples generated by two high-dimensional linear…

An important feature of linear mixed models and generalized linear mixed models is that the conditional mean of the response given the random effects, after transformed by a link function, is linearly related to the fixed covariate effects…

Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…

We consider the problem of quickly detecting a signal in a sensor network when the subset of sensors in which signal may be present is completely unknown. We formulate this problem as a sequential hypothesis testing problem with a simple…

We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero.…

This work proposes a research problem of finding sparse solution of undetermined Linear system with some applications. Two approaches how to solve the compressive sensing problem: using l_1 approach , the l_q approach with 0 < q < 1.…

This paper studies the validity of nonparametric tests used in the regression discontinuity design. The null hypothesis of interest is that the average treatment effect at the threshold in the so-called sharp design equals a pre-specified…

Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying…