Related papers: The Second Raabe's Test and Other Series Tests
To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests…
We introduce a notion of real-valued reward testing for probabilistic processes by extending the traditional nonnegative-reward testing with negative rewards. In this richer testing framework, the may and must preorders turn out to be…
Consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternative hypothesis $Q$, and only $P$…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
The quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
For $\chi^2-$tests with increasing number of cells, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients, we find necessary and…
Testing the (in)equality of variances is an important problem in many statistical applications. We develop default Bayes factor tests to assess the (in)equality of two or more population variances, as well as a test for whether the…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
In this work, we generalize the Cram\'er-von Mises statistic via projection-averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed…
We present a new way of testing ordered hypotheses against all alternatives which overpowers the classical approach both in simplicity and statistical power. Our new method tests the constrained likelihood ratio statistic against the…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack…
A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test against a constant function uses the…
Since the appearance of H. Robbins article (1948), the central limit theorems for random sums have been studied for about 70 years. The central limit theorems for random sums of independent random variables play a very important role in…
This paper develops inference methods for ratios of deterministic trend slopes in systems of pairs of time series. Hypotheses based on linear cross-equation restrictions are considered with particular interest in tests that trend ratios are…
This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
Higher criticism, or second-level significance testing, is a multiple-comparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance and one is interested in rejecting the…