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异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…

1963—1987年美国工资结构的变化：分位数回归的应用AI 解读

A recently developed quantile regression technique, which parsimoniously describes the entire conditional distribution, is applied to every March Current Population Survey since 1964. The study examines changes in the returns to schooling and experience at different points of the wage distribution and changes in within-group wage inequality. The results from the one-group and sixteen-group linear models show that the returns to schooling and experience differ across…

区间删失与截断观测下分布函数非参数估计的说明AI 解读

SUMMARY This paper is concerned with the nonparametric estimation of the distribution function F from interval-censored and truncated data as discussed by Turnbull. It is observed that Turnbull's characterization of F̂, the maximum likelihood estimator of F, is not applicable in general when the data are interval censored and truncated. It is shown, however, that Turnbull's characterization can be easily modified to obtain the appropriate characterization of F̂.

截断偏差与收入不平等的排序评价AI 解读

Lorenz dominance analysis is used to examine the effect of top-coding on the ordinal evaluation of U.S. income inequality across time. Current Population Survey microdata are adjusted for truncation bias, and statistical inference procedures are used to examine biennial changes in unadjusted and adjusted Lorenz curves. Beginning in 1985, the truncation bias has a significant effect on ordinal rankings of income inequality.

截断偏差与收入不平等的序数评价AI 解读

Lorenz dominance analysis is used to examine the effect of top-coding on the ordinal evaluation of U.S. income inequality across time. Current Population Survey microdata are adjusted for truncation bias, and statistical inference procedures are used to examine biennial changes in unadjusted and adjusted Lorenz curves. Beginning in 1985, the truncation bias has a significant effect on ordinal rankings of income inequality.

摘要暂缺

区间删失数据的最大似然：一致性与计算AI 解读

Standard convex optimization techniques are applied to the analysis of interval censored data. These methods provide easily verifiable conditions for the self-consistent estimator proposed by Turnbull (1976) to be a maximum likelihood estimator and for checking whether the maximum likelihood estimate is unique. A sufficient condition is given for the almost sure convergence of the maximum likelihood estimator to the true underlying distribution function.

基于枢轴估计函数的重抽样方法AI 解读

SUMMARY Suppose that, under a semiparametric model setting, one is interested in drawing inferences about a finite-dimensi onal parameter vector /? based on an estimating function. Generally a consistent point estimator /J for /?0, the true value for /J, can be easily obtained by finding a root of the corresponding estimating equation. To estimate the variance of ft, however, may involve complicated and subjective nonparametric functional estimates. In this paper, a general…

基于中位生存时间的期中分析AI 解读

For a typical two-arm survival study, analyses are usually performed periodically to evaluate, for example, the treatment difference. In this paper, we propose to use differences or ratios of estimated median survival times repeatedly during a study to evaluate the relative merit of two treatment groups. This new procedure provides quantitative assessments of the treatment difference and is completely model-free. Our method is illustrated with a recent aids clinical study…

最小α分位数估计的极小极大偏差性质AI 解读

A natural measure of the degree of robustness of an estimate $\mathbf{T}$ is the maximum asymptotic bias $B_\mathbf{T}(\varepsilon)$ over an $\varepsilon$-contamination neighborhood. Martin, Yohai and Zamar have shown that the class of least $\alpha$-quantile regression estimates is minimax bias in the class of $M$-estimates, that is, they minimize $B_\mathbf{T}(\varepsilon)$, with $\alpha$ depending on $\varepsilon$. In this paper we generalize this result, proving that the…

退化 U 统计量广义自助法的一致性AI 解读

A generalized bootstrap version is defined for degenerate $U$-statistics. Our main result shows that the (conditional) distribution function of the bootstrapped degenerate $U$-statistic provides a consistent estimator for the unknown distribution function of the degenerate $U$-statistic under consideration. For the proof we rely on a rank statistic approach.

L1回归估计量分布的解析与自助法近似AI 解读

Edgeworth and bootstrap approximations to estimator distributions in L1 regression are described. Analytic approximations based on Edgeworth expansions that mix lattice and nonlattice components and allow for an intercept term in the regression are developed under mild conditions, which do not even require a density for the error distribution. Under stronger assumptions on the error distribution, the Edgeworth expansion assumes a simpler form. Bootstrap approximations are…

Cox模型中随协变量变化的中位生存时间置信带AI 解读

Let ξp (x) be the pth quantile of the distribution of the life length of an individual with covariate vector x in the Cox model. We introduce an estimator ξp (x) of ξp (x) and develop several families of confidence bands for ξ(x) as a function of x. To construct one type of band, we proceed as follows. We show that as n → ∞, where n is the number of individuals in the study, ) converges weakly to a Gaussian process W(x) with a complicated covariance structure. We then…

利用提名样本估计分布函数AI 解读

A nomination sample consists of independently distributed maxima from subsamples of a population with the same underlying distribution. Nomination sampling occurs when only the item with largest value is chosen from each of n independent subsamples. If the subsamples differ in size, then these observed order statistics are not identically distributed, so estimation schemes built on assumptions of independently and identically distributed (iid) data are most likely…

中位绝对偏差的替代尺度估计量AI 解读

In robust estimation one frequently needs an initial or auxiliary estimate of scale. For this one usually takes the median absolute deviation MAD n = 1.4826 med, {|xi − med j x j |}, because it has a simple explicit formula, needs little computation time, and is very robust as witnessed by its bounded influence function and its 50% breakdown point. But there is still room for improvement in two areas: the fact that MAD n is aimed at symmetric distributions and its low (37%)…

利用提名样本估计分布函数AI 解读

A nomination sample consists of independently distributed maxima from subsamples of a population with the same underlying distribution. Nomination sampling occurs when only the item with largest value is chosen from each of n independent subsamples. If the subsamples differ in size, then these observed order statistics are not identically distributed, so estimation schemes built on assumptions of independently and identically distributed (iid) data are most likely…

摘要暂缺

贫困测度中的统计推断AI 解读

Several poverty indices have been suggested to measure the intensity of poverty suffered by those below the poverty line. Because the indices are estimated on the basis of sample observations, we need to test whether the observed differences in their values are statistically significant. This paper provides distribution-free asymptotic confidence intervals and statistical inference for additive poverty indices. The methodology developed in the paper is applied to analyze…

摘要暂缺

复合假设拟合优度检验的样本间距统计量大样本理论AI 解读

SUMMARY Let X 1,…, Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Often we would like to test a null hypothesis concerning the goodness of fit of F to some distribution function which is fully specified or belongs to some parametric family, i.e. in some applications the null hypothesis is simple whereas in others it may be composite. In this paper we present the large…

Jackknife 分布函数估计量的一项改进AI 解读

In a recent paper, C. F. J. Wu showed that the jackknife estimator of a distribution function has optimal convergence rate $O(n^{-1/2})$, where $n$ denotes the sample size. This rate is achieved by retaining $O(n)$ data values from the original sample during the jackknife algorithm. Wu's result is particularly important since it permits a direct comparison of jackknife and bootstrap methods for distribution estimation. In the present paper we show that a very simple,…

利用非参数回归估计有限总体分布函数AI 解读

This paper considers estimators of the distribution function of a variable over a finite population, when a sample of units is available and values of a related auxiliary variable are known for the whole population. Theory is offered for several estimators which rely on nonparametric regression, and for calibration estimators which require a parametric model.

分位数的平滑经验似然置信区间AI 解读

Standard empirical likelihood confidence intervals for quantiles are identical to sign-test intervals. They have relatively large coverage error, of size $n^{-1/2}$, even though they are two-sided intervals. We show that smoothed empirical likelihood confidence intervals for quantiles have coverage error of order $n^{-1}$, and may be Bartlett-corrected to produce intervals with an error of order only $n^{-2}$. Necessary and sufficient conditions on the smoothing parameter,…

L1 统计分析及相关方法AI 解读

Prologue. Thoughts on Real Data and Statistics (Y. Dodge). Some Statistical Tools for the Analysis of Complex Molecular Spectra (A.F. Ruckstuhl). Estimation, Testing and Property Characterization. The Gauss Markov Property for the Median (G.W. Basset, Jr.,). A Class of Estimators Based on Adaptative Convex Combinations of Two Estimation Procedures (Y. Dodge, J. Jureckova). Robustness of L1 Regression in the Light of Linear Programming (J. Dupacova). A Linear Model with a…