Related papers: Systematic errors in the maximum likelihood regres…
The spatial scan statistic is widely used in epidemiology and medical studies as a tool to identify hotspots of diseases. The classical spatial scan statistic assumes the number of disease cases in different locations have independent…
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…
This paper considers distributed estimation of linear systems when the state observations are corrupted with Gaussian noise of unbounded support and under possible random adversarial attacks. We consider sensors equipped with single…
Unambiguous detection of signals superimposed on unknown trends is difficult for unevenly spaced data. Here, we formulate the Discrete Chi-square Method (DCM) that can determine the best model for many signals superimposed on arbitrary…
With any symmetric distribution $\mu$ on the real line we may associate a parametric family of noncentral distributions as the distributions of $(X+\delta)^2$, $\delta\not=0$, where $X$ is a random variable with distribution $\mu$. The…
We propose a new approach for the problem of relative depth estimation from a single image. Instead of directly regressing over depth scores, we formulate the problem as estimation of a probability distribution over depth and aim to learn…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the…
We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman's and Pearson's chi-squares, namely "combined Neyman-Pearson chi-square" ($\chi^2_{\mathrm{CNP}}$). Through analytical…
The recently developed "Data Set Diagonalization" method (DSD) is applied to measure compatibility of the data sets that are used to determine parton distribution functions (PDFs). Discrepancies among the experiments are found to be…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…
The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application.…
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…
The Chain-Ladder (CL) method remains the dominant macro-level technique for claims reserving in non-life insurance, yet its classical formulation lacks a coherent probabilistic foundation. Existing stochastic extensions-including the Mack…
This paper introduces a quasi-likelihood ratio testing procedure for diffusion processes observed under nonsynchronous sampling schemes. High-frequency data, particularly in financial econometrics, are often recorded at irregular time…
Parton distributions functions (PDFs), which are essential to the interpretation of data from high energy colliders, are measured by representing them as functional forms containing many parameters. Those parameters are determined by…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
Given the vast reservoirs of data stored worldwide, efficient mining of data from a large information store has emerged as a great challenge. Many databases like that of intrusion detection systems, web-click records, player statistics,…
This paper gives a new approach for the maximum likelihood estimation of the joint of the location and scale of the Cauchy distribution. We regard the joint as a single complex parameter and derive a new form of the likelihood equation of a…