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High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to…
Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences…
In clinical trials the comparison of two different populations is a frequently addressed problem. Non-linear (parametric) regression models are commonly used to describe the relationship between covariates as the dose and a response…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
This paper introduces a framework for capturing stochasticity of choice probabilities in neural networks, derived from and fully consistent with the Random Utility Maximization (RUM) theory, referred to as RUM-NN. Neural network models show…
This paper proposes a new test for inequalities that are linear in possibly partially identified nuisance parameters. This type of hypothesis arises in a broad set of problems, including subvector inference for linear unconditional moment…
This paper provides a specification test for semiparametric models with nonparametrically generated regressors. Such variables are not observed by the researcher but are nonparametrically identified and estimable. Applications of the test…
This paper considers testing linear hypotheses of a set of mean vectors with unequal covariance matrices in large dimensional setting. The problem of testing the hypothesis $H_0 : \sum_{i=1}^q \beta_i \bmu_i =\bmu_0 $ for a given vector…
The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not…
This paper is about randomized iterative algorithms for solving a linear system of equations $X \beta = y$ in different settings. Recent interest in the topic was reignited when Strohmer and Vershynin (2009) proved the linear convergence…
This paper considers the learning of Boolean rules in disjunctive normal form (DNF, OR-of-ANDs, equivalent to decision rule sets) as an interpretable model for classification. An integer program is formulated to optimally trade…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
Fractional factorial designs are widely used for designing screening experiments. Nonregular fractional factorial designs can have better properties than regular designs, but their construction is challenging. Current research on the…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…
Exploiting symmetry inherent in data can significantly improve the sample efficiency of a learning procedure and the generalization of learned models. When data clearly reveals underlying symmetry, leveraging this symmetry can naturally…
In this paper, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…