Related papers: The Fisher score on the closed simplex
Combining dependent tests of significance has broad applications but the $p$-value calculation is challenging. Current moment-matching methods (e.g., Brown's approximation) for Fisher's combination test tend to significantly inflate the…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the…
Spectroscopy detected in the time domain entails many techniques, such as FTIR, pump-probe, FT-Raman, and 2DES, and applications, such as molecule characterization, excited state dynamics studies, or spectra classifications. Surprisingly,…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
I previously used Burgers' equation to introduce a new method of numerical discretisation of \pde{}s. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models all the processes and their…
The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying…
The standard simplex in R^n, also known as the probability simplex, is the set of nonnegative vectors whose entries sum up to 1. They frequently appear as constraints in optimization problems that arise in machine learning, statistics, data…
Single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and financial…
We introduce a semidefinite programming algorithm to find the minimal quantum Fisher information compatible with an arbitrary dataset of mean values. This certification task allows one to quantify the resource content of a quantum system…
In many statistical problems, the data distribution is specified through a generative process for which the likelihood function is analytically intractable, yet inference on the associated model parameters remains of primary interest. We…
Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of a…
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…
In proofs of L_2-differentiability, Lebesgue densities of a central distribution are often assumed right from the beginning. Generalizing Theorem 4.2 of Huber[81], we show that in the class of smooth parametric group models these densities…
This paper studies a regularized support function estimator for bounds on components of the parameter vector in the case in which the identified set is a polygon. The proposed regularized estimator has three important properties: (i) it has…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
Supervised learning models are one of the most fundamental classes of models. Viewing supervised learning from a probabilistic perspective, the set of training data to which the model is fitted is usually assumed to follow a stationary…
An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball…