Related papers: Critical issues with the Pearson's chi-square test
Let X_n=(x_{ij}) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that is, the entry…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
Empirical science needs to be based on facts and claims that can be reproduced. This calls for replicating the studies that proclaim the claims, but practice in most fields still fails to implement this idea. When such studies emerged in…
A fundamental property of QCD is the presence of the chiral anomaly, which is the primary component of the $\pi^0\rightarrow\gamma\gamma$ decay amplitude. Based on this anomaly and its small ($\simeq$ 4.5%) chiral correction, a firm…
Plausibility is a formalization of exact tests for parametric models and generalizes procedures such as Fisher's exact test. The resulting tests are based on cumulative probabilities of the probability density function and evaluate…
In this study, we focus on the likelihood ratio tests in the $p_0$ model for testing degree heterogeneity in directed networks, which is an exponential family distribution on directed graphs with the bi-degree sequence as the naturally…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
Meta-analysis combines results from multiple studies aiming to increase power in finding their common effect. It would typically reject the null hypothesis of no effect if any one of the studies shows strong significance. The partial…
We propose a new and rather stringent criterion for testing the goodness of fit between a theory and experiment. It is motivated by the paradox that the criterion on \chi^2 for testing a theory is much weaker than the criterion for finding…
We consider clinical trials with multiple, overlapping patient populations, that test multiple treatment policies specifically tailored to these populations. Such designs may lead to multiplicity issues, as false statements will affect…
Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P=Q. On the other hand, when comparing or testing particular parameters $\theta$ of P and Q, such as…
We consider a stationary linear AR($p$) model with observations subject to gross errors (outliers). The autoregression parameters as well as the distribution function (d.f.) $G$ of innovations are unknown. The distribution of outliers $\Pi$…
Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a P-value, we construct a…
The likelihood ratio test (LRT) and the related $F$ test, do not (even asymptotically) adhere to their nominal $\chi^2$ and $F$ distributions in many statistical tests common in astrophysics, thereby casting many marginal line or source…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
The robust Wald confidence interval (CI) for the Cox model is commonly used when the model may be misspecified or when weights are applied. However it can perform poorly when there are few events in one or both treatment groups, as may…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Determining the lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model. This paper proposes a non-inferiority test for the coefficient…
Positive predictive value and negative predictive value are two widely used parameters to assess the clinical usefulness of a medical diagnostic test. When there are two diagnostic tests, it is recommendable to make a comparative assessment…
The paper proposes chi-square and normal inference methodologies for the unknown coefficient matrix $B^*$ of size $p\times T$ in a Multi-Task (MT) linear model with $p$ covariates, $T$ tasks and $n$ observations under a row-sparse…