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小中样本下二乘二列联表中 Goodman–Kruskal Gamma 与 Spearman Rho 的分布AI 解读

The distribution of Goodman and Kruskal's G in 2 × 2 tables is examined for small and moderate sample sizes. A number of exact distributions are presented, and asymptotic results relevant to the speed of convergence of G to normality are given. Comparisons are made with the standard correlation coefficient r, It is concluded that the distribution of G converges to normality slowly in many cases and that its density function is irregular even for sample sizes as large as 50.

以预测分布函数误差最小化估计指数分布分位数AI 解读

We consider the problem of estimating the quantiles of a one-parameter exponential distribution. Using the estimated quantiles to predict the distribution function, and attempting to minimize mean square errors for these predicted probabilities rather than the quantiles themselves, we are led to estimators differing from the natural ones obtained by appropriate scaling of the estimated mean of the distribution. The form of these estimators is studied for complete and…

以预测分布函数误差最小化估计指数分布分位数AI 解读

We consider the problem of estimating the quantiles of a one-parameter exponential distribution. Using the estimated quantiles to predict the distribution function, and attempting to minimize mean square errors for these predicted probabilities rather than the quantiles themselves, we are led to estimators differing from the natural ones obtained by appropriate scaling of the estimated mean of the distribution. The form of these estimators is studied for complete and…

线性结构关系的大样本理论AI 解读

The sampling properties of estimators of the structural parameters in a linear structural relationship are studied, using the usual error-in-variables model. Under various assumptions about the error variances, large-sample variances, covariances and biases are found. The results depend critically on the sequences {n−1σ x2i and {n−1σ x2i}, where {xi are the true x-values, and when these can be regarded as sampled from some distribution with finite mean and variance these…

线性结构关系的大样本理论AI 解读

The sampling properties of estimators of the structural parameters in a linear structural relationship are studied, using the usual error-in-variables model. Under various assumptions about the error variances, large-sample variances, covariances and biases are found. The results depend critically on the sequences {n−1σ x2i and {n−1σ x2i}, where {xi are the true x-values, and when these can be regarded as sampled from some distribution with finite mean and variance these…

若干正态混合分布估计方法的比较AI 解读

Fisher's method of maximum likelihood breaks down when applied to the problem of estimating the five parameters of a mixture of two normal densities from a continuous random sample of size n. Two alternative methods, (i) moment estimates and (ii) multinomial maximum likelihood and niinimum x2 estimates obtained by grouping the underlying variable, are compared both for bias to n⊟θ1 and mean squared error to n⊟θ2 for a variety of mixed distributions. The methods do not differ…

矩估计量的偏差与准确性AI 解读

A new method for finding the biases and covariances of moment estimators to order n−2 is outlined and compared with existing solutions. It is thought that the new approach is likely to be particularly useful for cases where moment estimation is complicated. The application of the method to mixtures of normal distributions is considered in some detail and some numerical results are included.

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