Related papers: Asymptotic analysis for covariance parameter estim…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…
A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an…
This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…
We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…
We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth functionals (linear statistics) of the set of…
We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability of such an event, the extent to which the high…
We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to…
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…