Let X1, ... , Xn be n random variables, with cumulative distribution functions F1, ... , Fn. Define [xi]i: = Fi(Xi) for all i, and let [xi](1) [less-than-or-equals, slant] ... [less-than-or-equals, slant] [xi](n) be the order statistics of the ([xi]i)i. Let [alpha]1 [less-than-or-equals, slant]...

Bailey showed that the general pointwise forecasting for stationary and ergodic time series has a negative solution. However, it is known that for Markov chains the problem can be solved. Morvai showed that there is a stopping time sequence {[lambda]n} such that...

This paper concerns the rate of convergence in the central limit theorem for certain local dependence structures. The main goal of the paper is to obtain estimates of the rate in the multidimensional case. Certain one-dimensional results are also improved by using some more flexible...

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...

Let Y1,...,Yn be the order statistics of a simple random sample from a finite or infinite population, having median =M. We compare the variables Yj-M and Ym-M, where Ym is the sample median, that is, for odd n. The comparison is in terms of the likelihood ratio order, which implies stochastic...