8 problems

Let $p_{\min}=\min_{1\leqslant j\leqslant r}p_j>0$, let $\lambda\in\mathbb{R}$, and consider the high-probability bound for the Kolmogorov distance between the conditional distribu…

Let $v(a_i,b_i)=g(a_i-b_i)$ be a truncated convolutional-type exponential mechanism for a general function $g$, and consider the resulting Bahadur–Rao large deviation expansion, de…

Asymptotic normality conjecture.

Residual pseudo-likelihood validity conjecture. Other procedures using $\widehat{\alpha}_n$ will be valid under these assumptions.

Let $n$ denote the sample size and let $alpha$ denote the familywise error rate, with approximation formulas relating the familywise error rate to the pointwise type I error rate.…

Residuals are constructed from stationary marked Gibbs point processes using test functions and are evaluated over an expanding sampling window. A strong law of large numbers descr…

Bahadur-efficiency conjecture. The proposed test has high Bahadur efficiency in any case where it can be applied.

Applicability conjecture. Semi- and nonparametric generalized likelihood ratio statistics, score processes, and empirical likelihood could be used to build consistent data-driven N…