D. Such rules appear in problems related to the proof-reading process when we estimate the total number of errors n, the probabilities PI and P2, and the parameter A..
1 * can be represented in the form of conditions imposed on the family of distributions (Qp,,,, P E PJI). 6) and Ip == x(P) for a certain parameter x, then the problem considered consists in finding an unbiased estimator of x with uniformly minimal variance. 6) holds and the family PJI consists of one element only and the goal is to predict the values of a random variable I, then we deal with the probabilistic problem of finding the best mean-square predictor. In the present example we do not have to restrict ourselves to nonrandomized decision ru1es.
If n is not determined uniquely, then the rank r(i) of Wi is defined as the arithmetic mean of all the possible position numbers of Wi in the sequence (W1' ... , w,,) ordered nondecreasingly. > ... , w,,) = (r(1), ... , r(n)). , a realization is given as (W1> ... ,w,,) = (X1>Y1' ... ,X". YII). • , X,,(,,» is a sequence of order statistics for (Xl' ... , x,,), then (Ym1h ... , Y,,(n» is called the sequence of concomitants of the order statistics. We observe a sequence of values of the concomitants of order statistics.