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线性模型的 L 估计AI 解读

Linear combinations of order statistics, or L-estimators, have played an extremely important role in the development of robust methods for the one-sample problem. We suggest analogs of L-estimators for the parameters of the linear model based on the p-dimensional “regression quantiles” proposed by Koenker and Bassett (1978). A uniform, Bahadur-type asymptotic representation of regression quantiles is established, and this yields a general asymptotic theory of L-estimators…

由Pearson平方距离分量导出的检验统计量AI 解读

A general approach to the comparison of two absolutely continuous distributions is presented based on Pearson's θ2 measure. Although no simple estimates are available for θ2, it can be decomposed into components, all of which are easily estimated. Asymptotic distribution theory is derived for the component estimates, and the form of the components is considered for several standard problems. It is demonstrated that the components-of-θ2 approach provides a unified approach to…

概率与随机变量AI 解读

Probability Conditional probability and independence Random variables Continuous distributions Distribution function Functions of random variables Bivariate distributions Expectation of a random variable Variance of a random variable Moment generating functions Moments of bivariate distributions Probability generating functions Sums of random variables Unbiased estimators Sampling finite populations Generating random variables.

通过预枢轴化降低置信集的覆盖水平误差AI 解读

Approximate confidence sets for a parameter θ may be obtained by referring a function of θ and of the sample to an estimated quantile of that function's sampling distribution. We call this function the root of the confidence set. Either asymptotic theory or bootstrap methods can be used to estimate the desired quantile. When the root is not a pivot, in the sense of classical statistics, the actual level of the approximate confidence set may differ substantially from the…

非对称最小二乘估计与检验AI 解读

This paper considers estimation and testing using location measures for regression m odels that are based on an asymmetric least-squares criterion functio n. These estimators have properties that are analogous to regression quantiles, but are easier to calculate, as are the corresponding test statistics. Asymmetric least-squares tests of homoskedasticity and s ymmetry compare quite favorably with other tests of these hypotheses in terms of asymptotic relative efficiency.…

利用递减密度极大似然估计的均匀分布单调经验贝叶斯检验AI 解读

An empirical Bayes test for testing $\vartheta \leq \vartheta_0$ against $\vartheta > \vartheta_0$ for the uniform distribution on $\lbrack 0, \vartheta)$ is discussed. The relation is shown with the estimation of a decreasing density on $\lbrack 0, \infty)$ and a monotone empirical Bayes test is derived based on the least-concave majorant of the empirical distribution function. The asymptotic distribution of the Bayes risk is obtained and some Monte Carlo results are given.

列联表独立性的混合 Dirichlet 贝叶斯检验：稳健性与敏感性AI 解读

A mixed-Dirichlet prior was previously used to model the hypotheses of "independence" and "dependence" in contingency tables, thus leading to a Bayesian test for independence. Each Dirichlet has a main hyperparameter $\kappa$ and the mixing is attained by assuming a hyperprior for $\kappa$. This hyperparameter can be regarded as a flattening or shrinking constant. We here review the method, generalize it and check the robustness and sensitivity with respect to variations in…

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利用强单峰分布生成有序洛伦兹曲线族AI 解读

From any strongly unimodal density on the real line, it is possible to generate a one-parameter family of Lorenz curves. The resulting families of Lorenz curves are Lorenz ordered with respect to the indexing parameter. Symmetry of the unimodal density results in the generation of symmetric Lorenz curves. A related characterization of the normal distribution is presented.

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收入获得者群体之间相对经济富裕程度的测量AI 解读

This article introduces and discusses a new measure of the relative economic affluence (REA) between income distributions with different means. The REA measure D is applied to the U.S. white and black household income distributions of 1967 and 1979. The measure D shows that the REA of the white households with respect to the black households decreased from 1967 to 1979. This conclusion contrasts with those obtained by applications of distance or quasi-distance functions. It…

通过预枢轴化降低置信集的覆盖水平误差AI 解读

Approximate confidence sets for a parameter θ may be obtained by referring a function of θ and of the sample to an estimated quantile of that function's sampling distribution. We call this function the root of the confidence set. Either asymptotic theory or bootstrap methods can be used to estimate the desired quantile. When the root is not a pivot, in the sense of classical statistics, the actual level of the approximate confidence set may differ substantially from the…

N 个观测最大值的分位数估计AI 解读

Given independent and identically distributed random variables from an unknown distribution F, we want to estimate quantiles of FN. Using asymptotic extreme-value theory, two parametric approximations to FN are considered and approximate maximum likelihood estimates are obtained. Conditions for consistency and asymptotic normality of these estimates are given, and properties of the estimates are obtained through a small simulation study.

随机截断下乘积极限估计量的渐近性质AI 解读

Many authors have considered the problem of estimating a distribution function when the observed data is subject to random truncation. A prominent role is played by the product limit estimator, which is the analogue of the Kaplan-Meier estimator of a distribution function under random censoring. Wang and Jewell (1985) and Woodroofe (1985) independently proved consistency results for this product limit estimator and showed weak convergence to a Gaussian process. Both papers…

基尼系数与贫困指数：若干协调关系AI 解读

Poverty is usually defined as the extent to which individuals in a society or community fall below a minimal acceptable standard of living. An index of poverty is generally based on the proportion (α) of the poor people and their income distribution through the income gap ratio (β) (i.e., the average income gap of the poor people from the poverty line ω, taken as a ratio to ω itself) and other measures of income inequalities. In this context, the well-known Gini coefficient…

基于提名抽样的分布函数估计AI 解读

Nomination sampling is a sampling process in which every observation is the maximum of a random sample from some population. Assuming that all samples are taken from a single underlying distribution F, data may be viewed as consisting of pairs (Xi , Ki ), where Ki is the size of the ith sample and, given Ki = ki, Xi is distributed according to F ki. Willemain (1980), who discussed nomination sampling in the context of health care delivery, proposed an estimator for the…

基尼系数与贫困指数之间的协调关系AI 解读

Poverty is usually defined as the extent to which individuals in a society or community fall below a minimal acceptable standard of living. An index of poverty is generally based on the proportion (α) of the poor people and their income distribution through the income gap ratio (β) (i.e., the average income gap of the poor people from the poverty line ω, taken as a ratio to ω itself) and other measures of income inequalities. In this context, the well-known Gini coefficient…

利用调查数据估计分布函数AI 解读

A simple method for estimating population distribution functions and associated quantiles from sample survey data is described and some asymptotic theory for it presented. The method assumes a model-based approach to survey estimation and allows auxiliary population information to be directly incorporated into the estimation process. Monte Carlo results comparing the proposed method with conventional design-based methods are given. These suggest that the model-based approach…

超越对数模型中弹性估计量的置信区间AI 解读

This paper examines the distribution fu nctions of elasticity estimators in translog demand models. The authors consider the normaland ratio-of-normals distributions and present confidence intervals for the elasticity estimators. The results suggest that only elasticity estimato rs based on the means of the actual cost shares are likely to follow either the normal or ratio-of-normals distribution function. Examination of three published empirical studies demonstrates that…

有限总体抽样的贝叶斯统计推断AI 解读

Bayesian statistical inference for sampling a finite population is studied by using the Dirichlet-multinomial process as prior. It is shown that if the finite population variables have a Dirichlet-multinomial prior, then the posterior distribution of the inobserved variables given a sample is also Dirichlet-multinomial. If the population size tends to infinity (the sample size is fixed), sampling without replacement from a Dirichlet multinomial process is equivalent to the…

单峰分布函数的估计AI 解读

This paper deals with the problem of efficiently estimating (asymptotically minimax) a distribution function when essentially nothing is known about it except that it is unimodal. The sample distribution function $F_n$ is shown to be asymptotically minimax among the family $\mathscr{E}$ of all unimodal distribution functions. Since $F_n$ does not belong to this family, estimators belonging to this family are constructed and are shown to be asymptotically minimax relative to…

失效率递增分布的渐近极小极大估计量AI 解读

We construct nonparametric estimators of the distribution function F and its hazard function in the class of all increasing failure rate (IFR) distribution. Denoting the empirical distribution and empirical hazard function by $F_n$ and $H_n$ , respectively, let $C_n$ be the greatest convex minorant of $H_n$, and $G_n$ the distribution with hazard function $C_n$. The estimator $G_n$ is itself IFR. We prove that under suitable restrictions on F, and for any fixed $\lambda$ with…

线性回归模型中百分位数的置信带AI 解读

Simultaneous confidence intervals for percentiles of the normal regression model similar to those given by Steinhorst and Bowden (1971) are considered. Kanofsky's (1968) confidence band for a single normal distribution is modified and extended to the regression model. The confidence bands that are simultaneous in all percentiles provide corresponding confidence bands for the cumulative conditional normal distribution functions. The various procedures are compared with…