Related papers: Dos and don'ts of reduced chi-squared
The reduced chi-squared statistic is a commonly used goodness-of-fit measure, but it cannot easily detect features near the noise level, even when a large amount of data is available. In this paper, we introduce a new goodness-of-fit…
We demonstrate that two approximations to the chi^2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high counts…
Least-squares refitting is widely used in high dimensional regression to reduce the prediction bias of l1-penalized estimators (e.g., Lasso and Square-Root Lasso). We present theoretical and numerical results that provide new insights into…
If a discrete probability distribution in a model being tested for goodness-of-fit is not close to uniform, then forming the Pearson chi-square statistic can involve division by nearly zero. This often leads to serious trouble in practice…
I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between…
Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a…
Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information.…
This paper considers least-square based estimation of the amplitude and square amplitude of a quantized sine wave, done by considering random initial record phase. Using amplitude- and frequency-domain modeling techniques, it is shown that…
We study confidence regions and approximate chi-squared tests for variable groups in high-dimensional linear regression. When the size of the group is small, low-dimensional projection estimators for individual coefficients can be directly…
In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variable. We then consider the task of…
We give a general result on the effective degrees of freedom for nonlinear least squares estimation, which relates the degrees of freedom to the divergence of the estimator. We show that in a general framework, the divergence of the least…
Theoretical uncertainties in the predictions of relativistic mean-field models are estimated using a chi-square minimization procedure that is implemented by studying the small oscillations around the chi-square minimum. By diagonalizing…
In this paper, we develop new test statistics for private hypothesis testing. These statistics are designed specifically so that their asymptotic distributions, after accounting for noise added for privacy concerns, match the asymptotics of…
We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…
Weighted histograms are used for the estimation of probability density functions. Computer simulation is the main domain of application of this type of histogram. A review of chi-square goodness of fit tests for weighted histograms is…
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…
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.…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
Overparametrized interpolating models have drawn increasing attention from machine learning. Some recent studies suggest that regularized interpolating models can generalize well. This phenomenon seemingly contradicts the conventional…
With the advent of large-scale weak lensing surveys there is a need to understand how realistic, scale-dependent systematics bias cosmic shear and dark energy measurements, and how they can be removed. Here we describe how spatial…