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We deal with a planar random flight ${(X(t),Y(t)),0<tleq T}$ observed at $n+1$ equidistant times $t_i=iDelta_n,i=0,1,...,n$. The aim of this paper is to estimate the unknown value of the parameter $lambda$, the underlying rate of the Poisson process. The planar random flights are not markovian, then we use an alternative argument to derive a pseudo-maximum likelihood estimator $hat{lambda}$ of the parameter $lambda$. We consider two different types of asymptotic schemes and show the consistency, the asymptotic normality and efficiency of the estimator proposed. A Monte Carlo analysis for small sample size $n$ permits us to analyze the empirical performance of $hat{lambda}$. A different approach permits us to introduce an alternative estimator of $lambda$ which is consistent, asymptotically normal and asymptotically efficient without the request of other assumptions.
This paper is devoted to two different two-time-scale stochastic approximation algorithms for superquantile estimation. We shall investigate the asymptotic behavior of a Robbins-Monro estimator and its convexified version. Our main contribution is to
Nonparametric latent structure models provide flexible inference on distinct, yet related, groups of observations. Each component of a vector of $d ge 2$ random measures models the distribution of a group of exchangeable observations, while their dep
The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space. For the as
This work contributes to the limited literature on estimating the diffusivity or drift coefficient of nonlinear SPDEs driven by additive noise. Assuming that the solution is measured locally in space and over a finite time interval, we show that the
We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of expansion is n