Showing papers by "Herman Chernoff published in 1971"
01 Jan 1971
TL;DR: In this article, the authors present a rule for estimating a parameter by two instruments of unknown precisions in a one-armed and two-armed bandit problem, where the objective is to obtain an estimate of satisfactorily low variability with as little waste in sampling cost as possible.
Abstract: Publisher Summary This chapter discusses the efficient estimation of a parameter measurable by two instruments of unknown precisions. Let μ be the unknown value of a parameter for which an estimate is required. Suppose that this parameter may be measured by either of the two instruments whose precisions are not known in advance. It is desired to obtain an estimate of satisfactorily low variability with as little waste in sampling cost as possible. A rule for procedure is presented and evaluated in the context of normally distributed data. The rule used combines an approach used for stopping sampling in a one-sample problem and the solutions of a one-armed and two-armed bandit problem. It makes sense to use the nominal significance level in variations of the one-armed bandit problem where the data are not normally distributed and it is desired to maximize. Monte Carlo simulations have been carried out to measure the efficiency of the rule. The efficiency is measured by comparing the loss with the case where the precisions are known, in which case one can sample with the better instrument the appropriate number of times.
3 citations
15 Nov 1971
TL;DR: In this article, the mean of a normal distribution with known variance is estimated using k-order statistics from a large sample of n independent identically distributed random variables with unknown scale and location parameters, and linear unbiased estimates of these parameters can be constructed using k order statistics, where the orders are approximately ( lambda(1)n), (lambda(k)n) for specified lambda( 1), lambda(2),..., lambda(k).
Abstract: : Let X(1), X(2),...,X(n) be the order statistics from a large sample of n independent identically distributed random variables with unknown scale and location parameters. Linear unbiased estimates of these parameters can be constructed using k order statistics, where the orders are approximately (lambda(1)n), (lambda(k)n) for specified lambda(1), lambda(2),...,lambda(k). As k approaches infinity let the number of lambda(i) in an interval be proportional to a density function f. Then one may select f to yield approximately optimal spacings (i.e., choice of lambda(i)). The study is carried out for estimating the mean of a normal distribution with known variance. (Author)
3 citations