Related papers: Dos and don'ts of reduced chi-squared
We discuss the constraints one can place on cosmological parameters using current cosmic microwave background data. A standard $\chi^2$--minimization over band--power estimates is first presented, followed by a discussion of the more…
Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can…
Recently, there as been an increasing interest in the use of heavily restricted randomization designs which enforces balance on observed covariates in randomized controlled trials. However, when restrictions are strict, there is a risk that…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
Experimental datasets are growing rapidly in size, scope, and detail, but the value of these datasets is limited by unwanted measurement noise. It is therefore tempting to apply analysis techniques that attempt to reduce noise and enhance…
The assumption that a parametric class of functions fits the data structure sufficiently well is common in fitting curves and surfaces to regression data. One then derives a parameter estimate resulting from a least squares fit, say, and in…
We investigate the errors in modeling the redshift-space distortion (RSD) effect at large linear scales, using data from the Millennium simulation. While standard theoretical templates, such as the Kaiser formula and the TNS method, could…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
A prime goal of quantum tomography is to provide quantitatively rigorous characterisation of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the…
Two modifications of the chi square test for comparing usual(unweighted) and weighted histograms and two weighted histograms are proposed. Numerical examples illustrate an application of the tests for the histograms with different…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
Using multiple tracers of large-scale structure allows to evade the limitations imposed by sampling variance for some parameters of interest in cosmology. We demonstrate the optimal way of carrying out a multitracer analysis in a galaxy…
Pearson's chi-square tests are among the most commonly applied statistical tools across a wide range of scientific disciplines, including medicine, engineering, biology, sociology, marketing and business. However, its usage in some areas is…
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible…
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…
Regression with $\chi^2$ constructed from the covariance matrix should not be used for some combinations of covariance matrices and fitting functions. Using the technique for unsuitable combinations can amplify systematic errors. This…
We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not…
This paper analyses the effects of random noise in determining errors and confidence levels for galaxy redshifts obtained by cross-correlation techniques. The main finding is that confidence levels have previously been overestimated, and…