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In this work, pseudorandom sequence generators based on finite fields have been analyzed from the point of view of their cryptographic application. In fact, a class of nonlinear sequence generators has been modelled in terms of linear…
We develop and analyze a principled approach to kernel ridge regression under covariate shift. The goal is to learn a regression function with small mean squared error over a target distribution, based on unlabeled data from there and…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance…
The statistical analysis of univariate quantiles is a well developed research topic. However, there is a need for research in multivariate quantiles. We construct bivariate (conditional) quantiles using the level curves of vine copula based…
Counterfactual inference is a useful tool for comparing outcomes of interventions on complex systems. It requires us to represent the system in form of a structural causal model, complete with a causal diagram, probabilistic assumptions on…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
Capturing the conditional covariances or correlations among the elements of a multivariate response vector based on covariates is important to various fields including neuroscience, epidemiology and biomedicine. We propose a new method…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Studies often estimate associations between an outcome and multiple variates. For example, studies of diagnostic test accuracy estimate sensitivity and specificity, and studies of predictive and prognostic factors typically estimate…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…