Related papers: Trigonometrically approximated maximum likelihood …
We prove the asymptotic mixed normality of the least absolute deviation (LAD) estimator for a locally $\alpha$-stable stochastic differential equation (SDE) observed at high frequency, where $\alpha\in(0,2)$. We investigate both ergodic and…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…
Random graph mixture models are now very popular for modeling real data networks. In these setups, parameter estimation procedures usually rely on variational approximations, either combined with the expectation-maximisation (\textsc{em})…
This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…
Skew normal model suffers from inferential drawbacks, namely singular Fisher information in the vicinity of symmetry and diverging of maximum likelihood estimation. To address the above drawbacks, Azzalini and Arellano-Valle (2013)…
Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling the smoothness of the…
We prove asymptotic normality of the so-called maximum likelihood estimator of the extreme value index.
We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…
In this paper we study asymptotic properties of the maximum likelihood estimator (MLE) for the speed of a stochastic wave equation. We follow a well-known spectral approach to write the solution as a Fourier series, then we project the…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
It is shown the almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case. In this generalization, the step increases or decreases if the scalar product…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
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…
The goal of this paper is to construct ergodic estimators for the parameters in the double exponential Ornstein-Uhlenbeck process, observed at discrete time instants with time step size h. The existence and uniqueness, the strong…
We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) techniques which are of current interest in computational…
A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional…
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…
In the context of a large system of $N$ neurons interacting through spike events in a mean-field regime as $N\rightarrow \infty$, we characterize the estimation of a multidimensional parameter in the spiking rate, when the neural states are…
An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum…
While the asymptotic normality of the maximum likelihood estimator under regularity conditions is long established, this paper derives explicit bounds for the bounded Wasserstein distance between the distribution of the maximum likelihood…