Related papers: Dos and don'ts of reduced chi-squared
We forecast the future constraints on scale-dependent parametrizations of galaxy bias and their impact on the estimate of cosmological parameters from the power spectrum of galaxies measured in a spectroscopic redshift survey. For the…
A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional…
As it is well known, the standard deviation of a weighted average depends only on the individual standard deviations, but not on the dispersion of the values around the mean. This property leads sometimes to the embarrassing situation in…
We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of…
The weak lensing power spectrum carries cosmological information via its dependence on the growth of structure and on geometric factors. Since much of the cosmological information comes from scales affected by nonlinear clustering,…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
Knowledge of the noise distribution in magnitude diffusion MRI images is the centerpiece to quantify uncertainties arising from the acquisition process. The use of parallel imaging methods, the number of receiver coils and imaging filters…
It is known that modeling uncertainties and astrophysical foregrounds can potentially introduce appreciable bias in the deduced values of cosmological parameters. While it is commonly assumed that these uncertainties will be accounted for…
Linear noise-reduction filters used in spectroscopy must strike a balance between reducing noise and preserving lineshapes, the two conflicting requirements of interest.
How long after the merger of two black holes can one rely on linear perturbation theory, and how many quasinormal modes are in the ringdown? Such questions suggest that black hole spectroscopy suffers from systematic uncertainties that…
In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance,…
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
Weighted histograms in Monte Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiments with random events that have weights. In this paper, the bin contents of…
Heteroscedasticity is common in real world applications and is often handled by incorporating case weights into a modeling procedure. Intuitively, models fitted with different weight schemes would have a different level of complexity…
How can one meaningfully make a measurement, if the meter does not conform to any standard and its scale expands or shrinks depending on what is measured? In the present work it is argued that current evaluation practices for…
The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
This paper proposes minimum distance inference for a structural parameter of interest, which is robust to the lack of identification of other structural nuisance parameters. Some choices of the weighting matrix lead to asymptotic…
This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…
In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…