Related papers: Semiparametric Identification and Fisher Informati…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
We study here the difference between quantum statistical treatments and semi-classical ones, using as the main research tool a semi-classical, shift-invariant Fisher information measure built up with Husimi distributions. Its semi-classical…
A principled procedure to infer a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, from incomplete constraints, is presented. The inference process of the \textit{pdf}'s employs the Fisher information as…
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…
In quantum metrology, the parameter estimation accuracy is bounded by quantum Fisher information. In this paper, we present coherence measures in terms of (quantum) Fisher information by directly considering the post-selective non-unitary…
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…
Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…
Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement…
We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has…
The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…
We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak identification occurs when a parameter is weakly regular, i.e., when it is locally homogeneous of degree zero. When this happens,…
Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are able to learn high-dimensional systems from small data sets,…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Results by van der Vaart (1991) from semi-parametric statistics about the existence of a non-zero Fisher information are reviewed in an infinite-dimensional non-linear Gaussian regression setting. Information-theoretically optimal inference…
Many statistical estimands of interest (e.g., in regression or causality) are functions of the joint distribution of multiple random variables. But in some applications, data is not available that measures all random variables on each…
This paper considers the problem of estimation of the Fisher information for location from a random sample of size $n$. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…
We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…
Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially…
It is widely admitted that structured nonparametric modeling that circumvents the curse of dimensionality is important in nonparametric estimation. In this paper we show that the same holds for semi-parametric estimation. We argue that…