5 problems

In a multi-armed bandit experiment, suppose the strategy estimates the arms' variances during the experiment rather than assuming that they are known. Variance-estimation optimalit…

Let $\lambda \geq 0$ and $a_{\lambda} \geq 0$ be prespecified constants. Suppose $(\bar{\mathbf{x}}_T-\bar{\mathbf{x}}_C)\mid\mathbf{x}\sim\mathcal{N}(0,\mathbf{\Sigma})$, with…

Let $n$ be the size of a $d$-dimensional parameter space, and let $k$ trials of Latin Hypercube sampling be performed. For a $t$-dimensional subspace, write $P(k,n,d,t)$ for its co…

The optimal approximate designs for full interaction models are generated by the single sequence $[1\ 1\ 2\ 2]$ for $2\leq t\leq 30$, where $t$ denotes the number of treatments. Un…

Let $\mathit{BCD}(p)$ denote Efron's biased coin design, and let $\bolds{\Sigma}_{\mathbf{T}_n}$ be the covariance matrix associated with the treatment assignment vector for a samp…