Related papers: Parameter Estimation in Astronomy with Poisson-Dis…
Exact expressions are given for the distribution function of the ratio of a weighted sum of independent chi-squared variables to a single chi-square variable, scaled appropriately. This distribution is the generalization of the classical F…
Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…
Using Stein's method and the Malliavin calculus of variations, we derive explicit estimates for the Gamma approximation of functionals of a Poisson measure. In particular, conditions are presented under which the distribution of a sequence…
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…
There are several assumptions made in a standard $\chi^2$ analysis of data, including the frequent assumption that the likelihood function is well approximated by a multivariate Gaussian distribution. This article briefly reviews the…
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 $k \in \{0,1,...,N-1\}$…
We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and…
Data compression has become one of the cornerstones of modern astronomical data analysis, with the vast majority of analyses compressing large raw datasets down to a manageable number of informative summaries. In this paper we provide a…
I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find…
If monitoring Poisson count data for a possible mean shift (while the Poisson distribution is preserved), then the ordinary Poisson exponentially weighted moving-average (EWMA) control chart proved to be a good solution. In practice,…
The Poisson-Gamma model is a generalization of the Poisson model, which can be used for modelling count data. We show that the $D$-optimality criterion for the Poisson-Gamma model is equivalent to a combined weighted optimality criterion of…
Traditional binned statistics such as $\chi^2$ suffer from information loss and arbitrariness of the binning procedure. We point out that the underlying statistical quantity (the log likelihood $L$) does not require any binning beyond the…
The extraction of any physical information from quasielastic neutron scattering spectra is generally done by fitting a model to the data by means of chi-square minimization procedure. However, as pointed out by the pioneering work of D.S.…
We show for the first time that, under the null hypothesis of vanishing Granger causality, the single-regression Granger-Geweke estimator converges to a generalised $\chi^2$ distribution, which may be well approximated by a $\Gamma$…
A new method for including systematic errors in the regression with Poisson data is reviewed in this contribution, with emphasis on applications to astronomical spectra. The method consists of generalizing the usual Poisson log-likelihood,…
In order to carry out a systematic and thorough measurement of the HI Gunn-Peterson effect at high redshift, a quantitatively testable and repeatable procedure, in particular, a robust statistical weighting technique, is developed. It is…
[ABRIDGED] The Cash statistic, also known as the C stat, is commonly used for the analysis of low-count Poisson data, including data with null counts for certain values of the independent variable. The use of this statistic is especially…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
This paper presents the probability distribution function (p.d.f.) and cumulative distribution function (c.d.f.) of the weighted sum of central independent chi-squared random variables with non-zero weighs based on a method using moment…
The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated…