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We consider a doubly stochastic Poisson process with stochastic intensity $lambda_t =n qleft(X_tright)$ where $X$ is a continuous It^o semimartingale and $n$ is an integer. Both processes are observed continuously over a fixed period $left[0,Tright]$. An estimation procedure is proposed in a non parametrical setting for the function $q$ on an interval $I$ where $X$ is sufficiently observed using a local polynomial estimator. A method to select the bandwidth in a non asymptotic framework is proposed, leading to an oracle inequality. If $m$ is the degree of the chosen polynomial, the accuracy of our estimator over the Holder class of order $beta$ is $n^{frac{-beta}{2beta+1}}$ if $m geq lfloor beta rfloor$ and it is optimal in the minimax sense if $m geq lfloor beta rfloor$. A parametrical test is also proposed to test if $q$ belongs to some parametrical family. Those results are applied to French temperature and electricity spot prices data where we infer the intensity of electricity spot spikes as a function of the temperature.
In this paper, we deal with the problem of calibrating thresholding rules in the setting of Poisson intensity estimation. By using sharp concentration inequalities, oracle inequalities are derived and we establish the optimality of our estimate up to
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed parameter, is a
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic approximations of the m
The research described herewith is to re-visit the classical doubly robust estimation of average treatment effect by conducting a systematic study on the comparisons, in the sense of asymptotic efficiency, among all possible combinations of the estim
This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth is select