论文检索

以二元问题代替精确观测的样本划分AI 解读

The problem is to search for the t largest observations in a random sample of size n by asking binary-type questions of the people (or items) in the sample without collecting any exact data whatever. The unordered and ordered cases are both considered; in the latter case the complete ranking is of special interest. Two different criteria of optimality are considered: (a) to minimize the expected number of questions required and (b) to maximize the probability of terminating…

以二元问题代替精确观测的样本划分AI 解读

The problem is to search for the t largest observations in a random sample of size n by asking binary-type questions of the people (or items) in the sample without collecting any exact data whatever. The unordered and ordered cases are both considered; in the latter case the complete ranking is of special interest. Two different criteria of optimality are considered: (a) to minimize the expected number of questions required and (b) to maximize the probability of terminating…

多项分布与多个独立二项分布的可容许及极小极大估计AI 解读

Admissible and minimax estimation is discussed for estimating the parameters in the (a) multinomial distribution and in (b) $k$ independent binomial distributions. In (a) the loss function is $\sum^n_0\lbrack\delta_i(x) - \theta_i\rbrack^2/\theta_i$, where $\theta_0, \cdots, \theta_k(\sum\theta_i = 1)$ are the parameters in the multinomial distribution, and the estimators are restricted to $\sum^k_0\delta_i(x) = 1$. In (b) the loss functions considered are the weighted sum…

通过分组估计正态总体的百分位数AI 解读

In this article we apply the group-testing idea to the estimation of a percentile of a normal population when both the mean and the variance are unknown. The structure is such that we observe the sum of the normal, independent measurements of m units in one single observation (or test). Under the assumption of a fixed total cost T, we have obtained the optimal value of the group size m for both the small-sample and the large-sample (T → ∞) cases. Comparison with the…

通过分组测量估计正态总体分位点AI 解读

In this article we apply the group-testing idea to the estimation of a percentile of a normal population when both the mean and the variance are unknown. The structure is such that we observe the sum of the normal, independent measurements of m units in one single observation (or test). Under the assumption of a fixed total cost T, we have obtained the optimal value of the group size m for both the small-sample and the large-sample (T → ∞) cases. Comparison with the…

以概率估计为目标的群组检测AI 解读

The ideas of group testing, i.e. of testing units in batches instead of individually, where each test only indicates whether the tested baton contains only good units or whether it contains at least one defective, is applied to the problem of estimating the probability p of an arbitrary unit being defective. A certain class of nested halving procedures is shown to be highly efficient and the saving over the one-at-a-time procedures is even greater for the estimation problem…

摘要暂缺

与对照比较并划分多个正态总体的最优观测分配AI 解读

The optimal allocation of observations when several experimental populations are simultaneously compared with a control is discussed. Two optimal rules are considered: to minimize the expected number of populations misclassified and to maximize the probability of a correct decision. It is shown that these two rules are different, but that they are asymptotically equivalent as the total sample size becomes large.

摘要暂缺

摘要暂缺

共同方差未知时正态总体均值排序的两次抽样多重决策程序AI 解读

A multiple decision approach to the problem of ranking populations according to their population means has been formulated by Bechhofer (1954). A single-sample solution to this problem was presented by him for the case of normal populations with known variances. In the present paper the case of normal populations with unknown equal variances is considered. A two-sample procedure is proposed as a solution to the latter problem; this procedure is of the type used by Stein…

Student t 分布的二元推广及若干特殊情形的数值表AI 解读

A multivariate generelization of Stndent's t-distribution is considered. The bivariata case is treated in detail; exact and asymptotic expressions for the probability integral and an asymptotic expression for certain percentage points are obtained. The main results for the bivariate case are given as equations (10), (11), (23) and (30) below; these equations are used to construct tables for certain special cases.