arXiv subjects

Delphine Blanke

Publications and source records attributed to Delphine Blanke.

3 recordsLinked to original sources

arXiv2014

Weighted M-estimators for multivariate clustered data: theory and simulation results

We study weighted M-estimators for $\mathbb{R}^d$-valued clustered data and give sufficient conditions for their consistency. Their asymptotic normality is established with estimation of the asymptotic covariance matrix. We address the robustness of these estimators in terms of their breakdown point. Comparison with the unweighted case is performed with some numerical studies. They highlight that optimal weights maximizing the relative efficiency have a bad impact on the breakdown point.

math.ST↗

arXiv2014

Global smoothness estimation of a Gaussian process from regular sequence designs

We consider a real Gaussian process $X$ having a global unknown smoothness $(r_{\scriptscriptstyle 0},β_{\scriptscriptstyle 0})$, $r_{\scriptscriptstyle 0}\in \mathds{N}_0$ and $β_{\scriptscriptstyle 0} \in]0,1[$, with $X^{(r_{\scriptscriptstyle 0})}$ (the mean-square derivative of $X$ if $r_{\scriptscriptstyle 0}\ge 1$) supposed to be locally stationary with index $β_{\scriptscriptstyle 0}$. From the behavior of quadratic variations built on divided differences of $X$, we derive an estimator of $(r_{\scriptscriptstyle 0},β_{\scriptscriptstyle 0})$ based on - not necessarily equally spaced - observations of $X$. Various numerical studies of these estimators exhibit their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data.

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arXiv2013

Bayesian prediction for stochastic processes. Theory and applications

In this paper, we adopt a Bayesian point of view for predicting real continuous-time processes. We give two equivalent definitions of a Bayesian predictor and study some properties: admissibility, prediction sufficiency, non-unbiasedness, comparison with efficient predictors. Prediction of Poisson process and prediction of Ornstein-Uhlenbeck process in the continuous and sampled situations are considered. Various simulations illustrate comparison with non-Bayesian predictors.

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