Related papers: Remarks on a parameter estimation for von Mises--F…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and…
We propose improvements in numerical evaluation of symmetric stable density and its partial derivatives with respect to the parameters. They are useful for more reliable evaluation of maximum likelihood estimator and its standard error.…
Van Trees inequality, also known as the Bayesian Cram\'er-Rao lower bound, is a powerful tool for establishing lower bounds for minimax estimation through Fisher information. It easily adapts to different statistical models and often yields…
Contrary to the suggestion of Kitatani and Sinada (2000 J. Phys. A: Math. Gen. {\bf 33} 3545-3553), the scaling analysis of the order parameter distributions suggests the existence of a finite-temperature spin-glass phase transition $T_c\ne…
Skewed probit regression is but one example of a statistical model that generalizes a simpler model, like probit regression. All skew-symmetric distributions and link functions arise from symmetric distributions by incorporating a skewness…
In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…
This is a comment on publication in Phys. Rev. Lett. 90, 087205 (2003): ``Exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets: A `renormalized magnetic force theorem'''
A simple proof of a key inequality required by the paper's analysis is presented. An introductory section discussing the paper's setup may be helpful to some readers. An alternative statistical analysis is suggested.
Expert specialization is fundamental to Mixture-of-Experts (MoE) model success, yet existing metrics (cosine similarity, routing entropy) lack theoretical grounding and yield inconsistent conclusions under reparameterization. We present an…
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
This note presents a novel Bayesian attitude estimator with the matrix Fisher distribution on the special orthogonal group, which can smoothly accommodate both unit and non-unit vector measurements. The posterior attitude distribution is…
The possibility of construction of continuous analogue of Poisson distribution with the search of bounds of confidence intervals for parameter of Poisson distribution is discussed. Also, in the article is shown that the true value of a…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
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…
The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and…
We introduce a directed, weighted random graph model, where the edge-weights are independent and beta-distributed with parameters depending on their endpoints. We will show that the row- and column-sums of the transformed edge-weight matrix…
In this paper, we consider the problem of parameter estimating for a family of exponential distributions. We develop the improved estimation method, which generalized the James--Stein approach for a wide class of distributions. The proposed…
We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any…
In this paper, we propose a method based on GMM (the generalized method of moments) to estimate the parameters of stable distributions with $0<\alpha<2$. We don't assume symmetry for stable distributions.