Related papers: Primality tests, linear recurrent sequences and th…
A class of nonparametric two-sample tests has been proposed in this article. As a generalization of the original \v{S}id\'aks' test, the proposed test statistic is developed as the sum of the maximal precedence and maximal exceedance…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
A central question in mathematics and computer science is the question of determining whether a given ideal $I$ is prime, which geometrically corresponds to the zero set of $I$, denoted $Z(I)$, being irreducible. The case of principal…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…
This paper proposes a new class of nonparametric tests for the correct specification of models based on conditional moment restrictions, paying particular attention to generalized propensity score models. The test procedure is based on two…
We introduce credal two-sample testing, a new hypothesis testing framework for comparing credal sets -- convex sets of probability measures where each element captures aleatoric uncertainty and the set itself represents epistemic…
We introduce equivalence testing procedures for linear regression analyses. Such tests can be very useful for confirming the lack of a meaningful association between a continuous outcome and a continuous or binary predictor. Specifically,…
In statistics permutations typically arise in the context of rank plots for two-dimensional data. Such plots can also be interpreted as discrete copulas. In discrete mathematics, typically in the context of the description of large…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
In a recent letter, new representations were proposed for the pair of sequences ($\gamma,\delta$), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs ($\gamma,\delta$) labelled by the…
This paper highlights the emergence of the Omega sequence in number theory and its connection with the emergence of a new prime number, and also highlights its theoretical applications for Lucas-Lehmer primality test, and Euclid-Euler…
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…
We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests…
Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use,…
In this paper, we provide a generalization of Proth's theorem for integers of the form $Kp^n+1$. In particular, a primality test that requires only one modular exponentiation similar to that of Fermat's test without the computation of any…
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
A generalization of the well-known Fibonacci sequence is the $k$-Fibonacci sequence with some fixed integer $k\ge 2$. The first $k$ terms of this sequence are $0,0, \ldots, 1$, and each term afterwards is the sum of the preceding $k$ terms.…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for…