In this paper we consider a class of nonparametric estimators of a distribution function F, with compact support, based on the theory of IFSs. The estimator of F is tought as the fixed point of a contractive operator T defined in terms of a vector of parameters p and a family of affine maps W...

A subthreshold signal is transmitted through a channel and may be detected when some noise { with known structure and proportional to some level { is added to the data. There is an optimal noise level, called stochastic resonance, that corresponds to the highest Fisher information in the problem...

A problem of hypothesis testing is considered for a model of diffusion process with diusion coecient tending to zero. A simple hypothesis and a semiparametric alternative are formulated in the terms of the values of some functional of nonperturbed trajectory of the dynamical system. The test...

We consider a problem of estimation for the telegrapher’s processon the line, say X(t), driven by a Poisson process with non constantrate. It turns out that the finite-dimensional law of the process X(t)is a solution to the telegraph equation with non constant coefficients.We give the explicit...

We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called phi-divergence measures. By taking into account the quasi-likelihood approach developed for studying the...

We address a major discrepancy in matching methods for causal inference in observational data. Since these data are typically plentiful, the goal of matching is to reduce bias and only secondarily to keep variance low. However, most matching methods seem designed for the opposite problem,...

The LASSO is a widely used statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. We introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion...

In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete observations $\{X_{t_i}, i=0, \ldots, n\}$ with $t_i =...

In this paper we introduce the Random Recursive Partitioning (RRP) method. This method generates a proximity matrix which can be used in applications like average treatment effect estimation in observational studies. RRP is a Monte Carlo method that randomly generates non-empty recursive...

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$ is observed only when its path lies over some threshold $\tau$. On the basis of the observable part of the trajectory, the problem is to estimate finite dimensional parameter in both drift and diffusion coefficient under a discrete...