6 problems

Let $X_1,X_2,\ldots$ be a stationary ergodic process taking values in $\{1,\ldots,k\}$, and let $Y_1,Y_2,\ldots$ be conditionally independent given $X_1,X_2,\ldots$, with $Y_t$ con…

Let $f$ be a density on $\mathbb{R}^d$, and let $\{r_n\}$ be a sequence of radii satisfying $r_n=o(1)$ and … Let $\Delta_n$ denote the estimator used to prove the paper's first con…

Consider a hidden Markov model with trends, with true transition matrix $Q^*$ and maximum likelihood estimator $Q^{\hat{\theta}_n}$ based on the first $n$ observations. Let…

Comparability conjecture. Typically,

Vanishing inconsistency-region conjecture. As $k$ grows, the size of the area where Maximum Parsimony converges to the wrong tree converges to zero.

Arbitrary-tuple inconsistency conjecture. For every choice of $k$, there exists a number $n$ of sequences such that Maximum Parsimony is statistically inconsistent on $k$-tuple-sit…