Related papers: A multivariate normal approximation for the Dirich…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted $L^1$ and $L^\infty$ estimates. Furthermore, we…
This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong…
We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…
We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact…
Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\R^d$. We establish variance asymptotics as $n \to \infty$ for the re-scaled intrinsic volumes and $k$-face functionals of…
This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…
We derive the asymptotic expansion at infinity for embedded ends of uniformly elliptic Weingarten surfaces with finite total curvature in $\mathbb{R}^3$, and we establish a maximum principle at infinity. Furthermore, we solve the Dirichlet…
We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a Gaussian white noise experiment. Here,…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
The one-dimensional SDE with non Lipschitz diffusion coefficient $dX_{t} = b(X_{t})dt + \sigma X_{t}^{\gamma} dB_{t}, \ X_{0}=x, \ \gamma<1$ is widely studied in mathematical finance. Several works have proposed asymptotic analysis of…
Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…
We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…
We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…
We introduce a novel varying-weight dependent Dirichlet process (DDP) model that extends a recently developed semi-parametric generalized linear model (SPGLM) by adding a nonparametric Bayesian prior on the baseline distribution of the GLM.…
There exist multiple regression applications in engineering, industry and medicine where the outcomes follow an adaptive experimental design in which the next measurement depends on the previous observations, so that the observations are…