The longitudinal regression model $Z_i^j=m({\theta }_0,{𝕏}_i\left(T_i^j\right))+{\epsilon }_i^j,$ where $Z_i^j$ is the $j$th measurement of the $i$th subject at random time $T_i^j$, $m$ is the regression function, ${𝕏}_i\left(T_i^j\right)$ is a predictable covariate process observed at time $T_i^j$ and ${\epsilon }_i^j$ is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth $M$-estimator of unknown parameter ${\theta }_0$.

Real valued $M$-estimators ${\widehat{\theta }}_n:=min{\sum }_1^n\rho (Y_i-\tau \left(\theta \right))$ in a statistical model with observations $Y_i\sim F_{{\theta }_0}$ are replaced by ${ℝ}^p$-valued $M$-estimators ${\widehat{\beta }}_n:=min{\sum }_1^n\rho (Y_i-\tau \left(u\left(z_i^T\beta \right)\right))$ in a new model with observations $Y_i\sim F_{u\left(z_i^t{\beta }_0\right)}$, where $z_i\in {ℝ}^p$ are regressors, ${\beta }_0\in {ℝ}^p$ is a structural parameter and $u:ℝ\to ℝ$ a structural function of the new model. Sufficient conditions for the consistency of ${\widehat{\beta }}_n$ are derived, motivated by the sufficiency conditions for the simpler “parent estimator” ${\widehat{\theta }}_n$. The result is a general method of consistent estimation in a class of nonlinear (pseudolinear) statistical problems. If...

(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.

(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.

The paper investigates the relation between maximum likelihood and minimum $I$-divergence estimates of unknown parameters and studies the asymptotic behaviour of the likelihood ratio maximum. Observations are assumed to be done in the continuous time.

The paper investigates the relation between maximum likelihood and minimum $I$-divergence estimates of unknown parameters and studies the asymptotic behaviour of the likelihood ratio maximum. Observations are assumed to be done in the discrete time.

We study a minimum distance estimator in $L_2$-norm for a class ofnonlinear hyperbolic stochastic partial differential equations, driven by atwo-parameter white noise. The consistency and asymptotic normality of thisestimator are established under some regularity conditions on thecoefficients. Our results are applied to the two-parameterOrnstein-Uhlenbeck process.