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多部件应力—强度模型中的可靠性估计AI 解读

A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distributions are exponential with unknown scale parameters. The asymptotic distribution is obtained by expanding the unbiased estimate about the maximum likelihood value and establishing their…

配对比较最大似然排序的分支搜索算法AI 解读

An efficient algorithm is presented for solving a general class of mathematical programming problems. This class includes the specific task of finding a maximum likelihood ranking based on paired comparison data. It differs from a branch and bound scheme in that it searches the nodes of a tree one branch at a time. As a result, its time requirements appear to be better and its storage requirements are better than or as good as previous algorithms. An example from the…

摘要暂缺

球面上的对跖对称分布AI 解读

The distribution $\Psi(\mathbf{x}; Z, M) = \operatorname{const}. \exp(\mathrm{tr} (ZM^T \mathbf{xx}^T M))$ on the unit sphere in three-space is discussed. It is parametrized by the diagonal shape and concentration matrix $Z$ and the orthogonal orientation matrix $M. \Psi$ is applicable in the statistical analysis of measurements of random undirected axes. Exact and asymptotic sampling distributions are derived. Maximum likelihood estimators for $Z$ and $M$ are found and…

收入分布的便捷描述模型：伽马密度AI 解读

The distribution of personal income is approximated by a two-parameter gamma density function (Pearson Type III). The two parameters may be considered as indicators of scale and of inequality, respectively. Maximum likelihood estimates of the parameters are derived from a random sample using graphical techniques, and a likelihood ratio test for the hypothesis that the inequality parameter is the same for different distributions is presented. The derivation of both the…

摘要暂缺

相依观测的最大似然方法AI 解读

Summary Under certain conditions on conditional probability densities, in the case of dependent observations, the maximum-likelihood estimate is proved to be consistent, asymptotically efficient and asymptotically normal.

间接观测频数表的对数线性模型：最大似然方程AI 解读

Frequency tables are examined in which some cells are not distinguishable. Log-linear models are proposed for these tables which lead to likelihood equations closely related to those associated with log-linear models for conventional frequency tables. Just as in conventional tables, the maximum likelihood equations are shown to be the same under Poisson or multinomial sampling. Applications are made to the problem of estimation of gene frequencies from observed phenotype…

极值响应分布下的小样本升降法AI 解读

Tables for computing LD50 estimates are presented for the extreme value (smallest and largest) distributions based on maximum likelihood and minimum chi-square analyses for small sample up-and-down test outcome sequences of nominal length N, 2 ≤ N ≤ 6. Overall, especially considering the small sample sizes involved, LD50 estimates based on assumed symmetrical distributions seem relatively robust to minor departures from symmetry of the actual response distribution.

贝叶斯与非贝叶斯检验的折中：多项分布情形AI 解读

Compromises between Bayesian and non-Bayesian significance testing are exemplified by examining distributions of criteria for multinominal equiprobability. They include Pearson's X2, the likelihood-ratio, the Bayes factor F, and a statistic G that previously arose from a Bayesian model by “Type II Maximum Likelihood.” Its asymptotic distribution, implied by the theory of the “Type II Likelihood Ratio,” is remarkably accurate into the extreme tail. F too can be treated as a…

过度识别约束子集的检验AI 解读

A family of tests of significance is developed for coefficients in a single equation of a simultaneous system., Different members of this family are distinguished by the k-class estimator on which they are based, and on the alternative hypothesis against which they test. The size of the test is found when the disturbances are small, and the test is shown to be consistent if plim k = 1 or k = λ, the limited information maximum likelihood value.

逆二项抽样估计量的方差AI 解读

A closed form for the variance of the unbiased estimator of the proportion defective in a population, derived by inverse binomial sampling, is given. Comparisons are made with the maximum likelihood estimator which indicate that the unbiased estimator has greater efficiency and smaller mean squared error.

可接受性与统计推断AI 解读

The likelihood principle is criticized and the acceptability principle is enunciated. Most acceptable estimates are defined and some techniques for their calculation are developed. In the one-parameter case the most acceptable estimator is, under some conditions, median unbiased. Conditions for the strong consistency and asymptotic normality of the estimators are obtained. These are less stringent than those for the maximum likelihood estimator. An example is given where the…

联立方程系统中系数的有限信息最大似然估计分布的渐近展开AI 解读

An asymptotic expansion is made of the distribution of the limited information maximum likelihood estimate of the coefficient of one endogenous variable in an equation with two endogenous variables when the coefficient of the other endogenous variable is prescribed to be unity. The equation is one of a system of simultaneous equations, and all the predetermined variables in the system are assumed to be exogenous. The expansion in terms of the noncentrality parameter, which…

贝叶斯点估计量的抽样性质AI 解读

The sampling distributions of various Bayesian point estimators are examined and it is shown that by choosing an appropriate prior distribution for the unknown parameter such estimators can be less biased than the maximum likelihood estimator. It is also shown that a pivotal quantity can be developed by a suitable transformation of the unknown parameter.

由离散观测建模连续随机过程：太阳黑子数据应用AI 解读

Discretization of a continuous autoregressive moving average process at an equispaced sampling interval results in a discrete autoregressive moving average process. The relationship between the continuous and the discrete parameters yields a simple method of maximum likelihood estimation of the continuous parameters from a discretely sampled data. A technique is described for modeling of continuous processes from discrete observations and is illustrated with analysis of the…

分组对泊松参数极大似然估计方差与偏差的影响：蒙特卡洛结果AI 解读

In this article the effect of incomplete samples, grouped samples in particular, on the variance and bias of the estimator for the parameters from an underlying Poisson distribution is studied.

影响曲线及其在稳健估计中的作用AI 解读

This paper treats essentially the first derivative of an estimator viewed as functional and the ways in which it can be used to study local robustness properties. A theory of robust estimation “near” strict parametric models is briefly sketched and applied to some classical situations. Relations between von Mises functionals, the jackknife and U-statistics are indicated. A number of classical and new estimators are discussed, including trimmed and Winsorized means,…

贝叶斯点估计量的抽样性质AI 解读

The sampling distributions of various Bayesian point estimators are examined and it is shown that by choosing an appropriate prior distribution for the unknown parameter such estimators can be less biased than the maximum likelihood estimator. It is also shown that a pivotal quantity can be developed by a suitable transformation of the unknown parameter.

摘要暂缺

由离散观测建立连续随机过程模型：太阳黑子数据应用AI 解读

Discretization of a continuous autoregressive moving average process at an equispaced sampling interval results in a discrete autoregressive moving average process. The relationship between the continuous and the discrete parameters yields a simple method of maximum likelihood estimation of the continuous parameters from a discretely sampled data. A technique is described for modeling of continuous processes from discrete observations and is illustrated with analysis of the…

多个总体回归的分类与估计AI 解读

Two problems, classifying an individual into one of several populations and estimating the regression in that population, are simultaneously treated as one problem. This can be viewed as a problem of a missing observation on a categorical variable. When all variables are jointly distributed multivariate normal, the maximum likelihood solution is the intuitively appealing one: classify the individual using the usual likelihood ratio procedure, then estimate the regression…

位置未知的指数分布尺度参数的替代估计量AI 解读

Let $X_1, X_2,\cdots, X_n$ be independent observations from an exponential distribution with an unknown location-scale parameter $(\mu, \sigma)$. Let $\bar{X} = n^{-1} \sum X_i$ and $M = \min X_i$. Under squared error loss the best location-scale equivariant estimator of $\sigma$ is $\bar{X} - M$, which agrees with the maximum likelihood estimator. Arnold (J. Amer. Statist. Assoc. 65 (1970) 1260-1264) and Zidek (Ann. Statist. 1 (1973) 264-278) have shown that $\bar{X} - M$ is…

随机序约束下随机变量的最大似然估计AI 解读

Brunk, Franck, Hanson and Hogg (1966) ("Maximum likelihood estimation of the distributions of two stochastically ordered random variables," J. Amer. Statist. Assoc. 61 1067-1080) found and studied maximum likelihood estimates of a pair of stochastically ordered distribution functions. In this paper we discuss a generalization of this problem in which we do not require the domain of these "distribution functions" to be the real line. We think of the order restriction we…