Related papers: Integration by parts and representation of informa…
For a multidimensional It\^o semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated…
We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
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,…
A statistical framework is introduced for a broad class of problems involving synchronization or registration of data across a sensor network in the presence of noise. This framework enables an estimation-theoretic approach to the design…
In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…
By applying the formula for essential Whittaker functions established by Matringe and Miyauchi, we study five integral representations for irreducible admissible generic representations of ${\rm GL}_n$ over $p$-adic fields. In each case, we…
In this work, a generalised version of the central limit theorem is proposed for nonlinear functionals of the empirical measure of i.i.d. random variables, provided that the functional satisfies some regularity assumptions for the…
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…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…
Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas as they generally express the impossibility to have a complete description of a system via a finite number of information measures. In…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the…
Partial information decomposition (PID) of the multivariate mutual information describes the distinct ways in which a set of source variables contains information about a target variable. The groundbreaking work of Williams and Beer has…
The principal inertia components of the joint distribution of two random variables $X$ and $Y$ are inherently connected to how an observation of $Y$ is statistically related to a hidden variable $X$. In this paper, we explore this…
The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
Predicting scalar outcomes using functional predictors is a classic problem in functional data analysis. In many applications, however, only specific locations or time-points of the functional predictors have an impact on the outcome. Such…
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…