26 problems

John Thom measured the diameters of 33 Druid circles in Western Scotland and considered their integer-valued measurements in feet. Thom's conjecture. The diameters were intended to…

Let $X_1,\ldots,X_n$ be i.i.d. random variables with unknown density $s$ with respect to a measure $\nu$ on $(E,\mathcal{E})$. Let $h$ denote the Hellinger distance between densiti…

Dense-limit conjecture. Asymptotic distributions can be derived in the dense setting as well, which would further strengthen the results.

Motif-constraint testing conjecture. Formulating null hypotheses that constrain several motif counts simultaneously could yield tests for coefficient nullity in ERGMs.

Consider the empirical bootstrap and the independence bootstrap in the independence and regression settings, with sample size $n$ and parameter $b$. The empirical bootstrap is pair…

Universal testing-region conjecture. For any set, the testing region is always of the form

Nonsymmetric e-merging conjecture. Every admissible e-merging function, without assuming symmetry, should be a convex combination of a weighted average and the constant $1$.

Higher-order credal convergence conjecture.

Uniformity conjecture. When higher order credal sets contain all possible probability functions, the highest-order confidences converge to form a uniform distribution over the firs…

Consider two Gaussian random walks and an empirical kurtosis statistic formed from their paths. The numerator and denominator determining the limiting law of $\theta_n$ converge in…

Emmentaler chi-squared bound conjecture. There is a constant $C$ such that a bound of the form

Average distance test conjecture. Theorem 3.1 on the asymptotic power of the average distance test should also hold under this milder condition.

Consider prewhitening time series using autoregressive models $\operatorname{AR}(p)$ or autoregressive moving-average models $\operatorname{ARMA}(p,q)$, where $p$ and $q$ denote th…

The discussion concerns statistical tests for linear dependence between time series, including prewhitening, Granger causality, and $F$- or $\chi^2$-tests; autocorrelation in the u…

Classifier-dependent estimation-quality conjecture. The observed differences in test performance between classifiers are due to the quality of their estimates of the classification…

Let $H_0,H_1\subset\mathcal E$ be hypotheses for stationary ergodic distributions. A test is uniformly consistent if both errors converge to zero uniformly over the respective hypo…

Let $H_0$ and $H_1$ be hypotheses consisting of stationary ergodic distributions. A test is weakly asymmetrically consistent (respectively, weakly asymptotically consistent) when t…

Consider the conditional-copula test statistics and their bootstrapped versions, including the nonparametric-bootstrap constructions described in the paper. Let the other resamplin…

Let the conditional-copula tests be evaluated by bootstrap methods, and let the alternative resampling schemes be those proposed in Subsection. Bootstrap validity conjecture. The i…

Consider the test of $H_0:\alpha=\alpha_0$ against $H_1:\alpha\neq\alpha_0$ for $alpha_0\in(-1/2,1/4)$, with empirical rejection rates evaluated by Monte Carlo simulation at nomina…

Optimality conjecture. These lower bounds are optimal; that is, they determine the detection boundary.

In null-hypothesis significance testing, decisions based on convention are termed arbitrary or mindless, while decisions not based on convention may be termed subjective. Large sam…

Let $p$ be a positive integer that is not even, and consider the testing problem above with separation radius $\rho_n$. A consistent test is a test whose error probabilities tend t…

The test Th is one of the tests compared in simulations of two independent Poisson processes, alongside tests KS, Ne, G, and E. The tests G and E aggregate tests based on approxima…

A long-memory linear process is a process obtained by filtering iid innovations with coefficients whose dependence decays slowly over time. Chen and Deo's conjecture. The assumptio…