Related papers: Semiparametric Testing with Highly Persistent Pred…

We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…

In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

Statistical inference in parametric models (e.g., the Bradley--Terry model and its variants) for paired-comparison data has been explored in the high-dimensional regime, in which the number of items involving in paired comparisons diverges.…

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…

Nonresponse after probability sampling is a universal challenge in survey sampling, often necessitating adjustments to mitigate sampling and selection bias simultaneously. This study explored the removal of bias and effective utilization of…

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…

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…

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…

In many semiparametric models that are parameterized by two types of parameters---a Euclidean parameter of interest and an infinite-dimensional nuisance parameter---the two parameters are bundled together, that is, the nuisance parameter is…

The reliability of a high-throughput biological experiment relies highly on the settings of the operational factors in its experimental and data-analytic procedures. Understanding how operational factors influence the reproducibility of the…

This paper explores strong and weak consistency of M-estimators for non-identically distributed data, extending prior work. Emphasis is given to scenarios where data is viewed as a triangular array, which encompasses distributional…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss…

A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…

Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…