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The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in…
Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in $\mathbb{R}^\infty$ and related approximation properties are investigated using the popular…
It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based…
In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift…
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 paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and…
Decomposing a total causal effect into natural direct and indirect effects is central to revealing causal mechanisms. Conventional methods achieve the decomposition by specifying an outcome model as a linear function of the treatment, the…
In this paper, we study the linear transformation model in the most general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the…
In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many…
There are many approaches to nonlinear SEM (structural equation modeling) but it seems that a rather straightforward approach using Isserlis' theorem has not yet been investigated although it allows the direct extension of the standard…
Asymptotic distribution for the proportional covariance model under multivariate normal distributions is derived. To this end, the parametrization of the common covariance matrix by its Cholesky root is adopted. The derivations are made in…
We present a coherent Bayesian framework for selection of the most likely model from the five genetic models (genotypic, additive, dominant, co-dominant, and recessive) commonly used in genetic association studies. The approach uses a…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially…
In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form , and in each column the same variable appears. We also apply the algorithm to obtain a…
We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, and present a formula for the characteristic polynomial of the transition probability matrix of this CRW…
In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional…
Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…