Related papers: Fisher's Information for Discretely Sampled Levy P…
Efficient estimation of a non-Gaussian stable Levy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a…
We establish an expansion by Gamma-convergence of the Fisher information relative to the reference measure exp(-beta V), where V is a generic multiwell potential and beta goes to infinity. The expansion reveals a hierarchy of multiple…
We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…
Mimicking the maximum likelihood estimator, we construct first order Cramer-Rao efficient and explicitly computable estimators for the scale parameter $\sigma^2$ in the model $Z_{i,n}=\sigma n^{-\beta}X_i+Y_i,i=1,\ldots,n,\beta>0$ with…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as a suitable supremum. In addition, we enforce equivariance by a…
In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant, so reliable inference on the feature that controls jump…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…
The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…
Many real-world tasks include some kind of parameter estimation, i.e., determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic…
Basic general properties are considered for the Fisher-type information involving higher order derivatives. They are used to explore various properties of probability densities and to derive Stam-type inequalities.
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…
The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…
We develop the information geometry of L\'evy processes. Deriving $\alpha$-divergences directly in terms of the L\'evy triplets of the L\'evy processes, we identify Fisher information matrix and $\alpha$-connection on the statistical…
The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…