相关论文: Fixed-domain asymptotics for a subclass of Mat\'{e…
We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study…
We study local asymptotic properties of likelihood ratios of certain Heston models. We distinguish three cases: subcritical, critical and supercritical models. For the drift parameters, local asymptotic normality is proved in the…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
Non-Gaussian state-space models arise in several applications, and within this framework the binary time series setting provides a relevant example. However, unlike for Gaussian state-space models - where filtering, predictive and smoothing…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…
Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions…
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…
Variable selection for a multiple regression model (Noisy Linear Perceptron) is studied with a mean field approximation. In our Bayesian framework, variable selection is formulated as estimation of discrete parameters that indicate a subset…
Profile likelihoods are rarely used in geostatistical models due to the computational burden imposed by repeated decompositions of large variance matrices. Accounting for uncertainty in covariance parameters can be highly consequential in…
Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large excursion probabilities have been evaluated. Vector Gaussian…
Gaussian random fields are a powerful tool for modeling environmental processes. For high dimensional samples, classical approaches for estimating the covariance parameters require highly challenging and massive computations, such as the…
This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional…
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…