Related papers: On two-sided p-values for non-symmetric distributi…
Conditional specification of distributions is a developing area with many applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the…
Probability integral transforms (PITs) and empirical $p$-values are widely used to assess the calibration of predictive distributions. While exact PIT values are uniformly distributed under correct model specification, practical…
We develop the distribution of the number of hypotheses found to be statistically significant using the rule from Benjamini and Hochberg (1995) for controlling the false discovery rate (FDR). This distribution has both a small sample form…
Null hypothesis statistical significance testing (NHST) is the dominant approach for evaluating results from randomized controlled trials. Whereas NHST comes with long-run error rate guarantees, its main inferential tool -- the $p$-value --…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Forecasting and forecast evaluation are inherently sequential tasks. Predictions are often issued on a regular basis, such as every hour, day, or month, and their quality is monitored continuously. However, the classical statistical tools…
The energy test is a powerful binning-free, multi-dimensional and distribution-free tool that can be applied to compare a measurement to a given prediction (goodness-of-fit) or to check whether two data samples originate from the same…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
This paper discusses estimation and limited information goodness-of-fit test statistics in factor models for binary data using pairwise likelihood estimation and sampling weights. The paper extends the applicability of pairwise likelihood…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
A new standard is proposed for the evidential assessment of replication studies. The approach combines a specific reverse-Bayes technique with prior-predictive tail probabilities to define replication success. The method gives rise to a…
In this paper new test statistics are introduced and studied for the important problem of testing hypothesis that involves inequality constraint on proportions when the sample comes from independent binomial random variables: Wald type and…
We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for…
Empirical economic studies often involve multiple propositions or hypotheses, with researchers aiming to assess both the collective and individual evidence against these propositions or hypotheses. To rigorously assess this evidence,…
A pervasive issue in statistical hypothesis testing is that the reported $p$-values are biased downward by data "peeking" -- the practice of reporting only progressively extreme values of the test statistic as more data samples are…
In the field of multiple hypothesis testing, combining p-values represents a fundamental statistical method. The Cauchy combination test (CCT) (Liu and Xie, 2020) excels among numerous methods for combining p-values with powerful and…