Related papers: Maximum likelihood estimation for a bivariate Gaus…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
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…
Comparison of two univariate distributions based on independent samples from them is a fundamental problem in statistics, with applications in a wide variety of scientific disciplines. In many situations, we might hypothesize that the two…
In this note, we propose a new approach for the proof of the consistency and normality of the maximum likelihood estimator for nonlinear AR processes with markov-switching under the assumptions of uniform exponential forgetting of the…
The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures…
The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…
In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…
We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…
This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte…
The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…
The double Heston model is one of the most popular option pricing models in financial theory. It is applied to several issues such that risk management and volatility surface calibration. This paper deals with the problem of global…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…
A Markov-switching observation-driven model is a stochastic process $((S_t,Y_t))_{t \in \mathbb{Z}}$ where $(S_t)_{t \in \mathbb{Z}}$ is an unobserved Markov chain on a finite set and $(Y_t)_{t \in \mathbb{Z}}$ is an observed stochastic…
We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical…
A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and…
Full likelihood-based inference for high-dimensional multivariate extreme value distributions, or max-stable processes, is feasible when incorporating occurrence times of the maxima; without this information, $d$-dimensional likelihood…
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…