Related papers: Testing the statistical compatibility of independe…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
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…
We describe an apparently new measure of multivariate goodness-of-fit between sets of quantitative results from a model (simulation, analytical, or multiple regression), paired with those observed under corresponding conditions from the…
The coefficient of determination, known as $R^2$, is commonly used as a goodness-of-fit criterion for fitting linear models. $R^2$ is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case…
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…
The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
The Neyman-Pearson strategy for hypothesis testing can be employed for goodness of fit if the alternative hypothesis is selected from data by exploring a rich parametrised family of models, while controlling the impact of statistical…
Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…
Various distribution free goodness-of-fit test procedures have been extracted from literature. We present two new binning free tests, the univariate three-region-test and the multivariate energy test. The power of the selected tests with…
Empirical phi-divergence test-statistics have demostrated to be a useful technique for the simple null hypothesis to improve the finite sample behaviour of the classical likelihood ratio test-statistic, as well asfor model misspecification…
Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely…
Finding anonymization mechanisms to protect personal data is at the heart of recent machine learning research. Here, we consider the consequences of local differential privacy constraints on goodness-of-fit testing, i.e. the statistical…
Ordinal categorical data are widely collected in psychology, education, and other social sciences, appearing commonly in questionnaires, assessments, and surveys. Latent class models provide a flexible framework for uncovering unobserved…
We consider two division models for structured cell populations, where cells can grow, age and divide. These models have been introduced in the literature under the denomination of `mitosis' and `adder' models. In the recent years, there…
A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of $U$-empirical…
In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic…
We consider multinomial goodness-of-fit tests in the high-dimensional regime where the number of bins increases with the sample size. In this regime, Pearson's chi-squared test can suffer from low power due to the substantial bias as well…
Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…