Consider the stochastic processes X1, X2,... and [Lambda]1, [Lambda]2,... where the X process can be thought of as observations on the [Lambda] process. We investigate the asymptotic behavior of the conditional distributions of Xt+v given X1,..., Xt and [Lambda]t+v given X1,..., Xt with regard...

The change point problem for independent normal means is considered as a multiple testing problem. Two stepwise methods are considered. Namely, the binary segmentation method of Vostrikova (1981) [7] and the maximum residual down method of Cohen et al. (2009) [5]. Both of these methods are shown...

Suppose you observe a finite sequence of random variables from some known joint distribution F, you can stop the process at any time and your profit is the last observed value. If an optimal stopping rule is used, denote the expected profit by VF. What kind of ordering on multivariate...