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全有或全无依从下随机试验治疗疗效的非参数推断AI 解读

To evaluate the biological efficacy of a treatment in a randomized clinical trial, one needs to compare patients in the treatment arm who actually received treatment with the subgroup of patients in the control arm who would have received treatment had they been randomized into the treatment arm. In practice, subgroup membership in the control arm is usually unobservable. This paper develops a nonparametric inference procedure to compare subgroup probabilities with…

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…

多元统计中的缺失观测之四：简单线性回归札记AI 解读

In this note we examine the bias and small sample efficiency of certain estimators for the parameters of a linear regression function when some observations are missing. The estimators studies in this paper were suggested by the large sample study reported in this issue of the Journal. We conclude that our asymptotically unbiased estimators of β and μy | x have negligible bias in sample sizes as small as n = 20, and that our asymptotically unbiased estimator of σ2 may have…

多元统计中的缺失观测（三）：简单线性回归的大样本分析AI 解读

We derive the asymptotic distribution of several estimators for the parameters of the linear regression of y on x when some observations on y and on x are missing. Then, we compare estimators using a mean square error criterion. We find for example that a simple estimator of the linear regression function has asymptotic efficiency no worse than 0.95 compared with the maximum likelihood estimator (assuming bivariate normality) provided that no more than 30 per cent of the y's…

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Lehmann 两样本检验的小样本性质考察AI 解读

In this paper we examine how well the asymptotic null distribution of a two sample test due to Lehmann approximates the small sample distribution of the test, compare the validity of this Lehman test with the validity of the two sample t test under the null hypothesis of equal means, and compare the power of this Lehmannn test with the power of the t test. Our general conclusion is that experimenters will prefer to use the t test when the underlying distribution is the scale…

多元统计中的缺失观测（二）：简单线性回归的点估计AI 解读

We define and evaluate some simple estimators of the linear regression function of y and x, when observations may be missing on y or x. In particular, we compare the zero order estimator, a modified zero order estimator, and mixed estimators relative to the least squares estimator using the ratio of expected mean square errors as our measure of efficiency. Illustrative tables are given to support our conclusions regarding the estimator of choice.

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多元统计中的缺失观测Ⅰ：文献综述AI 解读

In this paper we review the literature on the problem of handling multivariate data with observations missing on some or all of the variables under study. We examine the ways that statisticians have devised to estimate means, variances, correlations and linear regression functions from such data and refer to specific computer programs for carrying out the estimation. We show how the estimation problems can be simplified if the missing data follows certain patterns. Finally,…

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