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逆线性回归问题的序贯解法AI 解读

In this note we apply the sequential theory developed by Chow and Robbins [1] and Gleser [3], [4] to the inverse linear regression problem. A two-stage sequential procedure has been proposed for the construction of a fixed-width confidence interval for $x$ (an unknown parameter). It is shown that the limiting probabilities of "correct decision" are equal to $P^\ast$ (pre-assigned).

最大参数的最优置信区间AI 解读

There are given k univariate distributions, indexed by a real-valued parameter θ, and k independent observations, one from each distribution. Let θ* denote the largest among the values of θ associated with the given distributions. This article is concerned with the estimation of θ*. A class of confidence intervals and a subclass of “optimal” confidence intervals for θ* are given. For a general class of distributions it is shown that the coverage probability of the confidence…

最大均值估计的渐近最优序贯程序AI 解读

Interval estimation of the largest mean of $k$ normal populations $(k \geqq 1)$ with a common variance $\sigma^2$ is considered. When $\sigma^2$ is known the optimal fixed-width interval is given so that, to have the probability of coverage uniformly lower bounded by $\gamma$ (preassigned), the sample size needed is minimized. This optimal interval is unsymmetric for $k > 2$. When $\sigma^2$ is unknown a sequential procedure is proposed and its behavior is studied. It is…

基于混合估计量的两个正态总体有序均值区间估计AI 解读

The interval estimation of ordered means of two normal populations based on a statistic which is sometimes the pooled sample mean and sometimes the maximum, or minimum, of the sample means, depending on whether the difference between the two sample means is small or large, when the two sample means have a common known variance is considered. The coverage probability of this procedure is derived and its behaviour is investigated. Comparisons with other procedures are made.

基于混合估计量的两个正态总体有序均值区间估计AI 解读

The interval estimation of ordered means of two normal populations based on a statistic which is sometimes the pooled sample mean and sometimes the maximum, or minimum, of the sample means, depending on whether the difference between the two sample means is small or large, when the two sample means have a common known variance is considered. The coverage probability of this procedure is derived and its behaviour is investigated. Comparisons with other procedures are made.

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.

多元正态与多元 t 分布的若干概率不等式AI 解读

Applying the result of expectations of non-negative random variables, inequalities for the one-sided and two-sided rectangular probabilities of higher-dimensional multivariate normal and multivariate t distributions are obtained. It is shown that their k-dimensional rectangular probabilities is lower bounded by the (k/m)th power of their m-dimensional rectangular probabilities for every k≥ m ≥ 1, and this bound is quite good when k/m is close to one. Applications to multiple…

多元正态与多元t分布的若干概率不等式AI 解读

Applying the result of expectations of non-negative random variables, inequalities for the one-sided and two-sided rectangular probabilities of higher-dimensional multivariate normal and multivariate t distributions are obtained. It is shown that their k-dimensional rectangular probabilities is lower bounded by the (k/m)th power of their m-dimensional rectangular probabilities for every k≥ m ≥ 1, and this bound is quite good when k/m is close to one. Applications to multiple…

多个正态总体最大均值的多阶段区间估计AI 解读

Summary We have k normal populations (k ⩾ 1) with means θ1, θ2, …, θk and a common unknown variance σ2. A fixed-width confidence interval for θ*=max⁡1≤i≤k θi is desired so that the coverage probability is at least γ (preassigned) for every θ = (θ1, θ2, …, θk) and σ2 > 0. A class of multistage procedures is considered for the solution of this problem. It is shown that at least for k ≤ 2, the efficiencies of those procedures are always less than one.

已知方差的多个正态总体最大均值的区间估计AI 解读

A procedure is given for the construction of a fixed-width confidence interval of the largest mean of k(k≥1) normal populations with a common known variance, based on the largest sample mean. The sample size required to achieve the preassigned confidence coefficient can be computed by using the standard normal table only.

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