Related papers: Maximum likelihood estimation for a bivariate Gaus…

In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbour balls are used as a multidimensional analogue to univariate spacings. A class of information-type measures is used to generalize the…

This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for…

The maximum likelihood estimate of the correlation parameter of a Gaussian process with and without of a nugget term is studied in the case of the analysis of deterministic models.

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…

The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small…

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian…

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…

In this paper, we study the maximum likelihood estimation of the parameters of the multivariate and matrix variate symmetric Laplace distributions through group actions. The multivariate and matrix variate symmetric Laplace distributions…

We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…

We study the maximum likelihood estimator of the location parameter of the Pearson Type VII distribution with known scale. We rigorously establish precise asymptotic properties such as strong consistency, asymptotic normality, Bahadur…

Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…

Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…

In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with…

This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a L\'{e}vy driven stochastic differential equation whose coefficients are…

We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…

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 nonsynchronous sampling of parameterized stochastic regression models, which contain stochastic differential equations. Constructing a quasi-likelihood function, we prove that the quasi-maximum likelihood estimator and the Bayes…