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We find that, in a linear model, the James-Stein estimator, which dominates the maximum-likelihood estimator in terms of its in-sample prediction error, can perform poorly compared to the maximum-likelihood estimator in out-of-sample…
While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper,…
We study global inference for regression coefficients in high-dimensional linear models under potentially heavy-tailed errors. While sum-type tests are powerful for dense alternatives and max-type tests excel for sparse alternatives,…
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
Testing large covariance matrices is of fundamental importance in statistical analysis with high-dimensional data. In the past decade, three types of test statistics have been studied in the literature: quadratic form statistics, maximum…
Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…
Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Rare and Weak models for multiple hypothesis testing assume that only a small proportion of the tested hypotheses concern non-null effects and the individual effects are only moderately large, so they generally do not stand out…
We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…
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…
This paper presents a theory of non-linear integer/real arithmetic and algorithms for reasoning about this theory. The theory can be conceived as an extension of linear integer/real arithmetic with a weakly-axiomatized multiplication…
We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly…
Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
Cauchy combination test has been widely used for combining correlated p-values, but it may fail to work under certain scenarios. We propose a truncated Cauchy combination test (TCCT) which focus on combining p-values with arbitrary…
Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and…
Machine learning models are usually evaluated according to the average case performance on the test set. However, this is not always ideal, because in some sensitive domains (e.g. autonomous driving), it is the worst case performance that…
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…
Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…