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单调百分位数回归AI 解读

Suppose that for each number $t$ in [0, 1] there is a distribution with distribution function $F_t(\bullet)$ which has $p$th percentile $\xi(t)$. Consider the problem of estimating $\xi(\bullet)$ under the assumption that $\xi(\bullet)$ is monotone. An estimator which is analogous to the median regression estimator considered in Cryer, Robertson, Wright and Casady (1972), is studied. Asymptotic properties including consistency and law of the iterated logarithm results are…

基于分组数据的洛伦兹曲线与基尼指数插值AI 解读

ECONOMISTS OFTEN SUMMARIZE the income distribution by the Lorenz curve and Gini index. A variety of parametric methods (e.g., [1 and 8]) have been developed to estimate these measures from the grouped income data governments provide (e.g., [3 and 12]). Previously, one of the authors developed a distribution-free approach [5] which yielded accurate bounds on the Gini index. While analogous bounds on the Lorenz curve can be obtained [5 and 10], the resulting curve is not…

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生物测定中 Spearman 型方差与百分位数估计量的性质AI 解读

Theoretical results for the Spearman-type variance estimator in the quantal response bioassay problem are determined when the mean of the underlying tolerance distribution is known, and also when it is unknown. For an experiment with infinitely many dose levels, the estimator is proved to be finite with probability one, and its mean and variance are given. Allowing the dose interval to approach zero, the estimator is shown to be asymptotically normal and asymptotically…

成对比较与多项比较模型的对数线性表示AI 解读

SUMAIARY This paper develops log linear model representations for the Bradley-Terry paired comparisons and Luce multiple comparisons models. Various multivariate extensions of the Bradley-Terry model are then considered. A model is presented, similar to one of Davidson & Bradley (1969), but which is based on the log odds ratio as a measure of association rather than the 0 coefficient of correlation. It is shown that, by the adaptive use of log linear model theory, complex…

若干广义线性模型最大似然估计的存在性与唯一性AI 解读

Generalized linear models were defined by Nelder & Wedderburn (1972) and include a large class of useful statistical models. It is shown that for some of these models maximum likelihood estimates always exist and that for some others they exist provided certain degeneracies in the data do not occur. Similar results are obtained for uniqueness of maximum likelihood estimates and for their being confined to the interior of the parameter space. For instance, with the familiar…

城市增长与迁移的联立方程模型AI 解读

The objectives of this study are twofold. First, a simultaneous-equations model that takes into account the interactions between various economic aspects of urban growth and migration to and from urban areas is specified. Second, the model is estimated for two different time periods, 1950–60 and 1960–70, with the Standard Metropolitan Statistical Area as the basic urban geographic unit. Included among the jointly dependent variables are civilian labor force out-migration,…

Logistic 回归与正态判别分析的效率比较AI 解读

A random vector x arises from one of two multivariate normal distributions differing in mean but not covariance. A training set x 1, x 2, ··· x n of previous cases, along with their correct assignments, is known. These can be used to estimate Fisher's discriminant by maximum likelihood and then to assign x on the basis of the estimated discriminant, a method known as the normal discrimination procedure. Logistic regression does the same thing but with the estimation of…

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城市增长与迁移的联立方程模型AI 解读

The objectives of this study are twofold. First, a simultaneous-equations model that takes into account the interactions between various economic aspects of urban growth and migration to and from urban areas is specified. Second, the model is estimated for two different time periods, 1950–60 and 1960–70, with the Standard Metropolitan Statistical Area as the basic urban geographic unit. Included among the jointly dependent variables are civilian labor force out-migration,…

终身收入估计的一项更正AI 解读

A reexamination is made of the formula for the variance of lifetime income in a stochastic process income distribution model. The formula in the received literature is shown to introduce a significant upward bias in estimates of this variance.

观察性研究的设计与分析：综述AI 解读

In recent years the number of studies which attempt comparisons without adequate randomization has increased rapidly, particularly in disciplines and areas of research involving human populations. This article highlights some of the more important developments (and emerging needs) in the design and analysis of such investigations. It provides a historical overview of those techniques adapted to bias reduction, covers recent developments in contingency table analysis,…

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柯布—道格拉斯生产函数的估计AI 解读

WE CONSIDER THE PROBLEM of estimating the coefficients of the Cobb-Douglas production function when observations are obtained from a cross section of firms. Under the assumptions that the firms operate in competitive markets and maximize actual profits, a stochastic model of production of the firms can be represented

利用分组数据界定分布矩AI 解读

This article derives bounds on a wide class of moments of the underlying distribution from data grouped in intervals when the mean of each group is given. The extremal distributions are constructed yielding the upper and lower bounds to moments of the form ∫h(x)dF(x), where h(x) is convex and F(x) is concave. To illustrate the results, bounds on the variance and Gini index are presented for two theoretical distributions.

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利用薪资数据估计百分位回归线AI 解读

In case of contamination, skewness or unequal variances, a nonparametric alternative to least squares regression is considered. In addition, investigators are often more interested in estimates of percentile lines than in the mean regression line. Thus, a modification of Brown-Mood regression is proposed to estimate the (100p) th percentile line α + βx of a random variable. This technique is applied to some data (artificial, but similar to real) relating the salary (y) of a…

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Some economic variables are restricted by an upper and lower limit but are continuous between the two limits. Measurements of such variables are sometimes available in their natural form and sometimes only in the form of three categories where information concerning the middle category is suppressed (unemployed, employed part time, employed full time, for example). Where such a variable is a continuous function of other variables between the two limits, the function can be…