5 problems

Let $Y_1,\ldots,Y_n$ be independent identically distributed samples from a Gaussian distribution, let $\mathbf{y}=(Y_1,\ldots,Y_n)$, let $\bar{\mathbf{y}}$ be their sample mean, an…

Let … be the related family of test statistics obtained by replacing the theoretical characteristic function in $T_{n,a}$ with its empirical counterpart. Analogue conjecture for…

Let $X$ have a non-degenerate non-normal distribution with existing moment generating function, and let $T_{n,\gamma}$ denote the test statistic defined in the paper for sample siz…

Consistency conjecture. Under any fixed alternative distribution,

Fixed-alternative limit conjecture. Denoting the right-hand side of (unglie) by $$ , we conjecture that