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Related papers: Chi-squared Test for Binned, Gaussian Samples

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This paper develops a set of test statistics based on bilinear forms in the context of the extremum estimation framework with particular interest in nonlinear hypothesis. We show that the proposed statistic converges to a conventional…

Econometrics · Economics 2021-08-10 Federico Crudu , Felipe Osorio

In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, they are not commonly used in empirical practice owing to features such as the non-pivotality of the test and the high computational cost of…

Econometrics · Economics 2025-12-23 Feiyu Jiang , Emmanuel Selorm Tsyawo

This paper discusses estimation and limited information goodness-of-fit test statistics in factor models for binary data using pairwise likelihood estimation and sampling weights. The paper extends the applicability of pairwise likelihood…

Methodology · Statistics 2026-03-30 Haziq Jamil , Irini Moustaki , Chris Skinner

Pearson's chi-squared test is widely used to assess the uniformity of discrete histograms, typically relying on a continuous chi-squared distribution to approximate the test statistic, since computing the exact distribution is…

Methodology · Statistics 2025-07-01 Nikola Banić , Neven Elezović

It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories minus 1 (assuming that no parameters are to be estimated --…

Statistics Theory · Mathematics 2014-10-28 Kris Duszak , Jan Vrbik

We detect and quantify significant numerical biases in the determination of the slope of power laws with Salpeter (or similar) indices from uniformly-binned data using chi-square minimization. The biases are caused by the correlation…

Astrophysics · Physics 2009-11-11 J. Maíz Apellániz , L. Úbeda

We consider the problem of estimating change in the dependency structure between two $p$-dimensional Ising models, based on respectively $n_1$ and $n_2$ samples drawn from the models. The change is assumed to be structured, e.g., sparse,…

Statistics Theory · Mathematics 2016-06-17 Farideh Fazayeli , Arindam Banerjee

Contemporary sample size calculations for external validation of risk prediction models require users to specify fixed values of assumed model performance metrics alongside target precision levels (e.g., 95% CI widths). However, due to the…

Applications · Statistics 2026-02-13 Mohsen Sadatsafavi , Paul Gustafson , Solmaz Setayeshgar , Laure Wynants , Richard D Riley

We consider whether the asymptotic distributions for the log-likelihood ratio test statistic are expected to be Gaussian or chi-squared. Two straightforward examples provide insight on the difference.

Data Analysis, Statistics and Probability · Physics 2017-12-13 Louis Lyons

This paper is concerned with the problem of conditional independence testing for discrete data. In recent years, researchers have shed new light on this fundamental problem, emphasizing finite-sample optimality. The non-asymptotic viewpoint…

Statistics Theory · Mathematics 2023-10-31 Ilmun Kim , Matey Neykov , Sivaraman Balakrishnan , Larry Wasserman

We have investigated a weighted chi-square distribution of the variable $\xi$ which is a weighted sum of squared normally distributed independent variables whose weights are cosines of angles $\phi_k=2\pi k/N$, where $k \in \{0,1,...,N-1\}$…

Disordered Systems and Neural Networks · Physics 2024-12-24 Vladislav Egorov , Boris Kryzhanovsky

We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of $\chi^2$-divergence on signed finite measures. The asymptotic…

Statistics Theory · Mathematics 2019-03-15 Salim Bouzebda , Amor Keziou

It is well-known that each statistic in the family of power divergence statistics, across $n$ trials and $r$ classifications with index parameter $\lambda\in\mathbb{R}$ (the Pearson, likelihood ratio and Freeman-Tukey statistics correspond…

Statistics Theory · Mathematics 2021-12-28 Robert E. Gaunt

Testing differences between a treatment and control group is common practice in biomedical research like randomized controlled trials (RCT). The standard two-sample t-test relies on null hypothesis significance testing (NHST) via p-values,…

Methodology · Statistics 2020-05-18 Riko Kelter

The aim of the current paper is to apply the method of Bambi (Bambi, 2015) to a source which contains two or more simultaneous triads of variability components. The joint chi-square variable that can be composed in this case, unlike some…

High Energy Astrophysical Phenomena · Physics 2023-11-10 Ivan Z. Stefanov

We analyze the complexity of Gibbs samplers for inference in crossed random effect models used in modern analysis of variance. We demonstrate that for certain designs the plain vanilla Gibbs sampler is not scalable, in the sense that its…

Computation · Statistics 2018-03-28 Omiros Papaspiliopoulos , Gareth O. Roberts , Giacomo Zanella

We provide necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives of chi-squared test for testing of hypothesis of homogeneity. The number of cells of chi-squared test increases with sample size…

Statistics Theory · Mathematics 2021-08-30 Mikhail Ermakov

Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…

Methodology · Statistics 2019-12-30 Luca Scrucca

The exact expression is derived for the expected value, $< {p_i}> $, for the parameter for any bin $i$ of a histogram following a multinomial distribution derived by sorting $N$ observations into bins of $B$ classes, if $n_i$ of the…

Statistics Theory · Mathematics 2013-03-18 Jonathan M. Friedman

For $m, d \in \mathbb{N}$, a jittered sample of $N=m^d$ points can be constructed by partitioning $[0,1]^d$ into $m^d$ axis-aligned equivolume boxes and placing one point independently and uniformly at random inside each box. We utilise a…

Probability · Mathematics 2022-09-13 Nathan Kirk , Florian Pausinger