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实验设计稳健性的新视角AI 解读

A common practical experimental philosophy when the underlying response model is unknown is initially to consider a first order model. A total robustness approach requires that the experimenter account for model underspecification due to possible curvature or interactions. It is reasonable that the experimental design possess protection against the selection of an oversimplified model. However, detection of possible underspecification is also important. This paper introduces…

实验设计稳健性的新视角AI 解读

A common practical experimental philosophy when the underlying response model is unknown is initially to consider a first order model. A total robustness approach requires that the experimenter account for model underspecification due to possible curvature or interactions. It is reasonable that the experimental design possess protection against the selection of an oversimplified model. However, detection of possible underspecification is also important. This paper introduces…

经典与现代回归及其应用AI 解读

The author emphasizes applications with examples that illustrate nearly all the techniques discussed. Applications have been selected from physical sciences, engineering, biology, management science and economics. Emphasis is also placed on concepts with a blend between illustrations using real data sets and mathematical and conceptual development. Expanded coverage includes: simultaneous influence, maximum likelihood estimation of parameters, and the plotting of residuals,…

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.

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离散概率函数线性组合的最大似然估计AI 解读

In this article the problem of obtaining the maximum likelihood estimates of the parameters from a special type of linear combination of discrete probability functions is discussed. It is shown that when the sample is completely categorized the estimation problem is no more complicated that that of estimating the parameters of each of the component probability functions separately. When the sample is less than completely classified an iterative procedure must be used to…

离散概率函数线性组合的最大似然估计AI 解读

In this article the problem of obtaining the maximum likelihood estimates of the parameters from a special type of linear combination of discrete probability functions is discussed. It is shown that when the sample is completely categorized the estimation problem is no more complicated that that of estimating the parameters of each of the component probability functions separately. When the sample is less than completely classified an iterative procedure must be used to…

分组泊松数据的极大似然估计AI 解读

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the…

分组 Poisson 数据的极大似然估计AI 解读

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the…

杂记：涉及方差分量假设的另一种近似F检验AI 解读

An alternative procedure is given to that presently used for assigning approximate degrees of freedom to the usual ratio of synthetic mean squares which is used as an approximate F statistic in analysis of variance. The standard procedure assigns pseudo degrees of freedom by treating the numerator and denominator separately, approximating each as a X2 distribution and equating the first two moments. Here the statistic is approximated directly as an F statistic. Monte Carlo…

涉及方差分量正线性组合的 Satterthwaite 检验替代方法AI 解读

This article proposes a refinement of the usual approximation due to Satterthwaite for making a significance test when the test statistic involves a single mean square in the numerator and a linear combination of mean squares in the denominator, that linear combination involving known positive constants. The test procedure is outlined in detail, and its derivation given in a separate section. The development of the technique essentially involves determining, by successive…

涉及方差分量正线性组合的 Satterthwaite 检验替代方法AI 解读

This article proposes a refinement of the usual approximation due to Satterthwaite for making a significance test when the test statistic involves a single mean square in the numerator and a linear combination of mean squares in the denominator, that linear combination involving known positive constants. The test procedure is outlined in detail, and its derivation given in a separate section. The development of the technique essentially involves determining, by successive…

样本变异系数的分位点AI 解读

This paper provides a simple formula for calculating percentage points of the sample coefficient of variation in the case of a normal parent distribution. The expression appears to be better than the existing approximations in the practical range of the population coefficient of variation V = óμ. The final product is a power series in V which agrees to four decimal places with an unpublished table of exact values.

样本变异系数的分位点计算AI 解读

This paper provides a simple formula for calculating percentage points of the sample coefficient of variation in the case of a normal parent distribution. The expression appears to be better than the existing approximations in the practical range of the population coefficient of variation V = óμ. The final product is a power series in V which agrees to four decimal places with an unpublished table of exact values.