Related papers: On the surjectivity of the conditional expectation…
We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…
In this paper, utilizing recent theoretical results in high dimensional statistical modeling, we propose a model-free yet computationally simple approach to estimate the partially linear model $Y=X\beta+g(Z)+\varepsilon$. Motivated by the…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Most research has focused on estimating the conditional average treatment…
We consider the problem of regression with selectively observed covariates in a nonparametric framework. Our approach relies on instrumental variables that explain variation in the latent covariates but have no direct effect on selection.…
This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…
If X and Y are real valued random variables such that the first moments of X, Y, and XY exist and the conditional expectation of Y given X is an affine function of X, then the intercept and slope of the conditional expectation equal the…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…
Let ${\mathfrak{G}}\subset\mathbb{R}^{3}$ with $vol(\mathfrak{G})\sim L^{3}$. Let ${\mathscr{T}}(x)$ be a Gaussian random field $\forall~x\in\mathfrak{G}$ with expectation $\mathbf{E}[{\mathscr{T}}(x)]=0$ and correlation…
Any Borel probability measure supported on a Cantor set of zero Lebesgue measure on the real line possesses a discrete inverse measure. We study the validity of the multifractal formalism for the inverse measures of random weak Gibbs…
We consider a Nonparametric Empirical Bayes (NPEB) framework. Let $Y_i$ be random variables, $Y_i \sim f(y|\theta_i)$, $i=1,...,n$, where $\theta_i \sim G$, and $\theta_i \in \Theta$ are independent. The variables $Y_i $ are conditionally…
We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these…
In this paper, we show that the G-normality of X and Y can be characterized according to the form of f such that the distribution of {\lambda}+f({\lambda})Y does not depend on {\lambda}, where Y is an independent copy of X and {\lambda} is…
We prove that the Young measure associated with a Borel function f is a probability distribution of the random variable f(U), where U has a uniform distribution on the domain of f. As an auxiliary result, the fact that Young measures…
We consider (annealed) large deviation principles for component empirical measures of several families of marked sparse random graphs, including (i) uniform graphs on $n$ vertices with a fixed degree distribution; (ii) uniform graphs on $n$…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power-laws. In this context q-expectation…
We study the weak convergence of conditional empirical copula processes, when the conditioning event has a nonzero probability. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general -…
We derive the probability distribution of product of two independent random variables, each distributed according the one-dimensional stable law. We represent the density by its power series and its asymptotic expansions. As Fox's…
In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied.…