Related papers: Cross-validation estimation of covariance paramete…
In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
Likelihood inference for max-stable random fields is in general impossible because their finite-dimen\-sional probability density functions are unknown or cannot be computed efficiently. The weighted composite likelihood approach that…
Mat\'ern random fields are one of the most widely used classes of models in spatial statistics. The fixed-domain identifiability of covariance parameters for stationary Mat\'ern Gaussian random fields exhibits a dimension-dependent phase…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
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…
We address the problem of upper bounding the mean square error of MCMC estimators. Our analysis is nonasymptotic. We first establish a general result valid for essentially all ergodic Markov chains encountered in Bayesian computation and a…
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…
The extremal dependence structure of a regularly varying $d$-dimensional random vector can be described by its angular measure. The standard nonparametric estimator of this measure is the empirical measure of the observed angles of the $k$…
We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean…
In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…