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合并二乘二列联表：估计量的渐近矩AI 解读

SUMMARY Consider J independent pairs of mutually independent binomial variates which can be considered as 72 times 2 tables. We assume a common measure of association, such as the odds ratio, between the tables. This paper studies the asymptotic moments of the ‘pooled' estimators, i.e. those constructed from the data summed over all the tables. For balanced designs, or proportional subclass numbers, it is shown that the pooled estimator of the common odds ratio is…

列联表单元近似均值的两种修正之间的等价性AI 解读

Stevens (1951) gives approximate expressions for the conditional mean and variance of an entry in a contingency table with fixed marginals. Cornfield (1956) shows these to be the moments of the asymptotic normal approximation to the noncentral hypergeometric distribution. McCullagh (1984) and Levin (1984) suggest corrections to the expression for the mean. We show that the bias correction preferred by Levin for the conditional case is virtually identical to that derived by…

列联表单元格近似均值的两种修正之等价性AI 解读

Stevens (1951) gives approximate expressions for the conditional mean and variance of an entry in a contingency table with fixed marginals. Cornfield (1956) shows these to be the moments of the asymptotic normal approximation to the noncentral hypergeometric distribution. McCullagh (1984) and Levin (1984) suggest corrections to the expression for the mean. We show that the bias correction preferred by Levin for the conditional case is virtually identical to that derived by…

二项随机变量对数的偏差与高阶累积量AI 解读

The bias and first four cumulants of the distribution of the logarithm of a binomial variate are studied by means of asymptotic expansions and exact computation. A new estimator of the variance is derived and evaluated. The asymptotic skewness is found to differ from the result of Walter (1975). Applications to point estimation of the one-hit curve and the interval estimation and testing of the ratio of binomial parameters are considered. Because of the bias and nonnormality…

二项随机变量对数的偏差与高阶累积量AI 解读

The bias and first four cumulants of the distribution of the logarithm of a binomial variate are studied by means of asymptotic expansions and exact computation. A new estimator of the variance is derived and evaluated. The asymptotic skewness is found to differ from the result of Walter (1975). Applications to point estimation of the one-hit curve and the interval estimation and testing of the ratio of binomial parameters are considered. Because of the bias and nonnormality…

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The bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation. The covariance of the empirical logit and its estimated variance is derived. Neither the +½ correction of Haldane (1955) and Anscombe (1956) nor the −½ suggested by Cox (1970) for weighted logit regression is universally effective in reducing bias. Other corrections are considered. The distribution of the empirical…

多个二乘二列联表共同相对风险的近似检验与区间估计AI 解读

Consider I pairs of mutually independent binomial variates xoi and x1i, with corresponding parameters poi and p1i and sample sizes, noi and n1,, where i = 1, ..., I. We assume that the relative risk is constant, that is, b = Pt /izpoi (i = 1, ..., I). Further let qji = 1-pji, and we assume throughout that 0 < pji, qji < 1 for i = 1, ..., I and j = 0,1. We consider asymptotic results as noi's and n1j's become large, but I is fixed. Extending the results of Cochran (1954) for…

经验 logit 的偏差、方差估计、偏度和峰度对加权最小二乘分析的影响AI 解读

The bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation. The covariance of the empirical logit and its estimated variance is derived. Neither the +½ correction of Haldane (1955) and Anscombe (1956) nor the −½ suggested by Cox (1970) for weighted logit regression is universally effective in reducing bias. Other corrections are considered. The distribution of the empirical…

某些共同相对风险或优势比非迭代估计量的渐近无效率AI 解读

Nurminen (1981) gives conditions for the asymptotic efficiency of general weighted mean estimators. His application is a noniterative estimator of a common relative risk for binomial variates. This summary estimator and, by implication, the Mantel-Haenszel summary odds ratio estimator are asserted to be asymptotically efficient. We examine conditions for the asymptotic efficiency in the unconditional sample space of the Mantel Haenszel estimator for a common odds ratio, the…

某些共同相对风险或优势比非迭代估计量的渐近无效率性AI 解读

Nurminen (1981) gives conditions for the asymptotic efficiency of general weighted mean estimators. His application is a noniterative estimator of a common relative risk for binomial variates. This summary estimator and, by implication, the Mantel-Haenszel summary odds ratio estimator are asserted to be asymptotically efficient. We examine conditions for the asymptotic efficiency in the unconditional sample space of the MantelHaenszel estimator for a common odds ratio, the…

2 × s × t 列联表的交互作用检验AI 解读

SUMMARY The interaction test for 2 x 2 x t contingency tables of Zelen (1971) is extended to 2 x 8 x t tables. This test is related to the tests of partial association, or 'main effect', of Birch (1965) and Armitage (1966). These tests are frequency analogues of the log-frequency tests con- sidered by Plackett (1962) and Goodman (1964). The various analyses are illustrated and compared in several numerical examples. Bartlett (1935) considered a model and statistical analysis…

零截断二项分布若干估计量的小样本表现AI 解读

Estimation of the parameter of a binomial distribution with the zero class truncated is a classical problem in human genetics. Mathematically the problem is the estimation of p from n, independent observations with distribution, (r s)prqs-r/(1 - qs) where r = 1, 2, ··· s, q = 1 - p and s ≥ 2 is a known integer. This article gives exact results which show the simple estimator of Mantel [17] to be less biased, both asymptotically and in small samples, than either the ML…

零截断二项分布若干估计量的小样本表现AI 解读

Estimation of the parameter of a binomial distribution with the zero class truncated is a classical problem in human genetics. Mathematically the problem is the estimation of p from n, independent observations with distribution, (r s)prqs-r/(1 - qs) where r = 1, 2, ··· s, q = 1 - p and s ≥ 2 is a known integer. This article gives exact results which show the simple estimator of Mantel [17] to be less biased, both asymptotically and in small samples, than either the ML…

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交叉设计中比较配对比例的精确检验AI 解读

SUMMARY An exact test for comparing proportions in matched samples is derived for the situation where order within pairs may be important. The analysis is based on an extension of the logistic model of Cox (1958 c). The test is formally equivalent to Fisher's exact test for 2 x 2 tables. The McNemar test (1947) has long been used in comparing matched or paired responses each of which take only two values, 0 or 1. The test consists of counting only those pairs which are…

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多种 logit 及其方差估计量的偏差：量反应生物测定应用AI 解读

SUMMARY The bias of several logit estimators and their corresponding variance estimators is investigated in small samples. Their use in quantal bioassay is similarly explored. The logit transformation has been suggested in the analysis of higher dimensional contingency tables, by Woolf (1954) and many others more recently, and also in estimating the parameters of the logistic function in the quantal bioassay problem (Berkson, 1944, 1953). Various modifications of the logit…

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相对风险的近似置信限AI 解读

SUMMARY The relative risk or odds ratio has been proposed as one alternative to the difference in proportions in measuring the degree of association in two by two tables. This paper proposes two new methods for finding confidence limits on the relative risk, one appropriate for large numbers, and a second for small numbers. The first is related to the usual chi-square test and the second to an approximation to the Fisher-Irwin test. The methods are compared to those…

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