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特定协方差矩阵的表示及其渐近效率应用AI 解读

Although maximum likelihood estimates are asymptotically efficient, they are often very hard to find. Replacement of some, but not all, of the equations in the maximum likelihood system may make it more manageable. The covariance matrices of the new estimator and of the estimating functions will have special structure in relation to the information matrix. These relationships are characterized and various properties that pertain to multiparameter efficiency are developed.…

比较多个相关比例的检验的渐近功效AI 解读

The limit distribution of Cochran's Q statistic for testing the equality of k proportions in matched samples is obtained for sequences of Pitman alternatives. Comparison of the asymptotic power of the test based on the Q statistic with that of the test based on Wald's statistic for the same asymptotic level shows that neither test is uniformly better than the other. We study by simulation a modified Q test using an estimated critical value obtained from a Satterthwaite-type…

分类误差下不保持的层级对数线性模型AI 解读

A model of Bross (1954) for classification error in 2 × 2 contingency tables is extended to higher dimensional tables. It is known (Mote and Anderson 1965) that the usual hypothesis tests of independence for a sampled two-dimensional table have the nominal significance level in the presence of misclassification. A simple criterion is given to determine which hierarchical log-linear models in higher dimensional tables do not share this property, that is, are not preserved by…

多项分布的极化检验AI 解读

A multinomial distribution with k cells is said to be polarized if the total probability mass of the distribution is essentially concentrated into a fewer number of cells. In this article a criterion is developed for measuring polarization, and a statistical test is given for testing the hypothesis that a multinomial distribution has a given measure of polarization against the alternative hypothesis that the measure of polarization is larger. The given test is called a…

对数似然的凹性AI 解读

For a very general regression model with an ordinal dependent variable, the log likelihood is proved concave if the derivative of the underlying response function has concave logarithm. For a binary dependent variable, a weaker condition suffices, namely, that the response function and its complement each have concave logarithm. The normal, logistic, sine, and extreme-value distributions, among others, satisfy the stronger condition, the t (including Cauchy) distributions…

比率与回归估计量的渐近分布AI 解读

We give a formal derivation of the asymptotic normality of ratio and regression estimators of a finite population total for simple random sampling and for sampling with probability proportional to aggregate size. The results are all well known and widely used, of course, but a rigorous development, spelling out relatively simple sufficient conditions under which the standard results are valid, does not seem to be available at present.

比率估计量及其方差估计量的实证研究AI 解读

This paper reports results from an empirical study of the ratio estimator for a finite population total. From each of six real populations, 1,000 simple random samples, 1,000 restricted random samples, and three nonrandom samples of size 32 are drawn. Performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using (a) prediction (superpopulation) models and (b) probability sampling distributions. The results,…

非对称时间序列AI 解读

Asymmetric time series respond to innovations with one of two different rules according to whether the innovation is positive or negative. Quoted industrial prices are apparently such a series. It has been observed that when market conditions change, quoted prices are not revised immediately. This delay operates more strongly against reductions in price quotations than against increases. A statistical model for such asymmetric times series is developed and analyzed. An…

未知均匀分布下的极小极大停止规则AI 解读

An invariance-based method of obtaining the minimax stopping rule when sampling from an unknown uniform distribution is presented and applied to two problems, maximizing the probability of selecting the smallest observation and minimizing the expected quantile of the observation selected. In the first problem, the minimax rules use only the relative ranks of the observations; in the second problem they are shown to achieve asymptotic risk (3 + 2 √2)1/√2/n ≈ 3.4780/n, which…

利用均值先验假说的泊松均值联合估计AI 解读

Estimators are presented for the simultaneous estimation of p means of Poisson variables. These have significantly smaller mean square errors of estimation in the region of a pre-specified set of values, and are conservative, in the sense that their mean errors are never worse than that of the minimum variance unbiased estimator, when p > 3.

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若干岭估计量的模拟研究AI 解读

Ridge regression, which defines a class of estimators indexed by a biasing parameter k, is an alternative to least squares estimation in the multiple linear regression model. Many algorithms for the biasing parameter have been proposed in the statistical literature. The present study identifies 10 promising algorithms and systematically evaluates and compares them using Monte Carlo methods. Three algorithms perform well overall. A two-parameter estimator offers potential…

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低响应概率下逻辑回归的样本量计算AI 解读

The Fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented Hessian matrix of the moment-generating function for the covariates. The approximation is valid when the probability of response is small. With its use one can obtain a simple closed-form estimate of the asymptotic covariance matrix of the maximum likelihood parameter estimates, and thus approximate sample sizes needed to test hypotheses about the…

三种数据驱动非参数概率密度估计方法的蒙特卡洛研究AI 解读

Although the theoretical properties of modern nonparametric probability density estimators have been studied for 25 years, there remains the practical problem of how to specify the amount of bias or smoothing in a density estimate based on a random sample. In this paper we review and evaluate three recently developed data-based algorithms that completely specify a density estimate from a random sample. Using Monte Carlo techniques, we compare the statistical accuracy of…

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应用概率导论AI 解读

Designed for a curriculum that contains only 2 single one-semester course on probability. Covers the core of probability theory, considers sums of random variables, derives sampling distributions, and discusses the approximation of distributions. Includes nonstatistical and statistical applications such as hypothesis testing, confidence intervals, and regression analysis. Numerous worked examples throughout the text illustrate the material and each chapter concludes with a…

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某类协方差矩阵的表示及其渐近效率应用AI 解读

Although maximum likelihood estimates are asymptotically efficient, they are often very hard to find. Replacement of some, but not all, of the equations in the maximum likelihood system may make it more manageable. The covariance matrices of the new estimator and of the estimating functions will have special structure in relation to the information matrix. These relationships are characterized and various properties that pertain to multiparameter efficiency are developed.…

摘要暂缺

分类错误下不被保持的层级对数线性模型AI 解读

A model of Bross (1954) for classification error in 2 × 2 contingency tables is extended to higher dimensional tables. It is known (Mote and Anderson 1965) that the usual hypothesis tests of independence for a sampled two-dimensional table have the nominal significance level in the presence of misclassification. A simple criterion is given to determine which hierarchical log-linear models in higher dimensional tables do not share this property, that is, are not preserved by…

多项分布的极化检验AI 解读

A multinomial distribution with k cells is said to be polarized if the total probability mass of the distribution is essentially concentrated into a fewer number of cells. In this article a criterion is developed for measuring polarization, and a statistical test is given for testing the hypothesis that a multinomial distribution has a given measure of polarization against the alternative hypothesis that the measure of polarization is larger. The given test is called a…