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恰好识别情形下 LIML 与 2SLS 结构系数分布函数的说明AI 解读

Many alternative techniques of estimating coefficients appearing in the structural representation of econometric models have been developed. The techniques of two-stage least squares (2SLS) and limited information maximum likelihood (LIML) yield identical estimates in the exactly identified case. The derivations of the density functions of these estimators for overidentified structural equations do not formally include the exactly identified case. In this note we demonstrate…

恰好识别情形下 LIML 与 2SLS 结构系数分布函数札记AI 解读

Many alternative techniques of estimating coefficients appearing in the structural representation of econometric models have been developed. The techniques of two-stage least squares (2SLS) and limited information maximum likelihood (LIML) yield identical estimates in the exactly identified case. The derivations of the density functions of these estimators for overidentified structural equations do not formally include the exactly identified case. In this note we demonstrate…

用混合Edgeworth–鞍点展开近似条件分布AI 解读

Conditional density and distribution functions can be approximated by the mixed Edgeworth-saddlepoint expansion. This technique is briefly described, and its use and character are illustrated by three examples concerning miscellaneous exponential families of order two.

Goodness-of-fit tests are given for the logistic distribution, based on statistics calculated from the empirical distribution function. Emphasis is on the statistics W2, U2 and A2, for which asyinptotio percentage points are given, for each of the three cases where one or both of the parameters of the distribution must be estimated from the data. Slight modifications of the calculated statistics are given to enable the points to be used with small samples. Monte Carlo…

依据危险率比较两个概率分布的分布无关检验AI 解读

Let F(x) and G(x) be the absolutely continuous distribution functions of two life distributions with rF(x) and rG(x) as their respective hazard rates. In the class of increasing failure rate distributions, one-sided scale as well as one-sided location alternatives imply that one hazard rate is uniformly smaller than the other. A new distribution-free test for testing H0 : rF(x) = rG(x) against HA: rF(x) ≤ rG(x) has been proposed. The test is seen to possess robust asymptotic…

非参数贝叶斯区间估计AI 解读

Bayesian confidence bands for a distribution function are converted into confidence intervals for specified population quantilea and also for the mean. Bayesian tolerance limits are similarly constructed.

基于泊松过程方差—时间曲线的随机性检验AI 解读

Summary In an earlier paper, the author shows that a suitably normalized estimator η^0 of the variance-time curve of a Poisson process is asymptotically normal as the time of observation of the process increases. In this paper, the distributions of the functionals ζ^1c=∫01η^c(t) and ζ^2c=∫01[η^c(t)]2 are obtained, and computing formulae for the sample analogues are provided. The first is normally distributed. For the second, which is reminiscent of the Cramer-von Mises…

Let $X_1, \cdots, X_n$ be an ordered sample from a distribution $A_n$ on [0, 1]. The $k$-spacings $D_1(N, k), \cdots, D_N(N, k)$ are defined and the weak convergence of their empirical distribution function under a sequence of alternatives $A_n$ approaching the uniform distribution is established. This is then applied to find the limiting distribution of $W_n(g, k) = N^{-\frac{1}{2}}\Sigma^N_{i=l}(g(NkD_i(N, k)) - a)$ where $g$ is a smooth function and $k$ is fixed. The…

百分位曲线的同时估计及其薪资数据应用AI 解读

A nonparametric iterative method is proposed for the simultaneous estimation of percentile curves. The method provides good descriptive statistics for salary data for which the assumptions of normality and equal variance are usually not valid. The method, a modified counting procedure based on minimum chi-squared estimation, is related to ordinary least squares through grafted polynomials and works even for nonlinear percentile curves.

百分位曲线的同时估计及其薪资数据应用AI 解读

A nonparametric iterative method is proposed for the simultaneous estimation of percentile curves. The method provides good descriptive statistics for salary data for which the assumptions of normality and equal variance are usually not valid. The method, a modified counting procedure based on minimum chi-squared estimation, is related to ordinary least squares through grafted polynomials and works even for nonlinear percentile curves.

泊松与正态均值的星形序列估计AI 解读

A vector $\mu = (\mu_1, \cdots, \mu_n)$ is said to be upper [lower] starshaped if $\mu_{m + 1} \geqslant 0 \lbrack \leqslant \mu_{m + 1} \leqslant \bar{\mu}_m\rbrack m = 1, \cdots, n - 1$, where $\bar{\mu}_m$ is a weighted average of $\mu_1, \cdots, \mu_m$. Obtained is the maximum likelihood estimate of $\mu$ when the $\mu_i$'s are the means of $n$ Poisson or normal populations and $\mu$ is known to be starshaped. The method is applied to obtain estimators of IHRA…

单峰密度下由分组数据界定矩、基尼指数与洛伦兹曲线AI 解读

In this article we first show how to extend the method for bounding ∫ h(x)f(x)dx from data grouped in intervals in which h(x) is convex and f(x) is decreasing to the case in which f(x) is unimodal. We then show that the unimodal density functions that bound ∫ h(x)f(x)dx for any convex function h(x) also bound the Gini index and the Lorenz curve.

财富分布模型AI 解读

The paper presents a model of wealth distribution that makes use of Gibrat's law of proportionate effect to explain the way wealth is distributed and how the distribution changes over time. The stochastic factor in each period is shown to be the result of deliberate choices by individual decision makers regarding their savings, investment, and bequests, given their inherited wealth and natural ability. The source of randomness is two-fold: uncertainty about the rates of…

渐进删失检验中若干分位数过程的弱收敛AI 解读

For progressive censoring schemes pertaining to a general class of (parametric as well as nonparametric) testing situations, one encounters a (partial) sequence of linear combinations of functions of order statistics where the coefficients are themselves stochastic variables. Weak convergence of such a quantile process to an appropriate Gaussian function is studied here, and the same is incorporated in the formulation of suitable (time-) sequential tests based on these…

标准化经验过程上确界的渐近分布AI 解读

The supremum of the empirical distribution function $F_n$ centered at its expectation $F$ and standardized by division by its standard deviation has recently been shown by Jaeschke to have asymptotically an extreme-value distribution after a second location and scale transformation depending only on the sample size $n$. In this paper the studentized form of the above statistic, obtained by division by the estimated standard deviation, is shown to have the same large sample…

子区间上标准化经验分布函数上确界的渐近分布AI 解读

It is well known that the limit distribution of the supremum of the empirical distribution function $F_n$ centered at its expectation $F$ and standardized by division by its standard deviation is degenerate, if the supremum is taken on too large regions $\varepsilon_n < F(u) < \delta_n$. So it is natural to look for sequences of linear transformations, so that for given sequences of sup-regions $(\varepsilon_n, \delta_n)$ the limit of the transformed sup-statistics is…

收入增长对分组收入分布、对应洛伦兹曲线与基尼指数的影响AI 解读

The purpose of this paper is to indicate the problems connected with the intertemporal comparability of Lorenz curves and Gini indices estimated by standard numerical approaches in the case of the classified empirical income distribution and a growth of individual income at a fixed rate. Collector effects of the higher intervals lead to shifts of the Lorenz curve to the right or to the left; accordingly the Gini index may rise or fall. This class phenomenon occurs although…

摘要暂缺

非参数贝叶斯区间估计AI 解读

SUMMARY Bayesian confidence bands for a distribution function are converted into confidence intervals for specified population quantiles and also for the mean. Bayesian tolerance limits are similarly constructed.

用混合 Edgeworth–鞍点展开近似条件分布AI 解读

Conditional density and distribution functions can be approximated by the mixed Edgeworth-saddlepoint expansion. This technique is briefly described, and its use and character are illustrated by three examples concerning miscellaneous exponential families of order two.

基于经验分布函数的逻辑斯蒂分布拟合优度检验AI 解读

Goodness-of-fit tests are given for the logistic distribution, based on statistics calculated from the empirical distribution function. Emphasis is on the statistics W2, U2 and A2, for which asyinptotio percentage points are given, for each of the three cases where one or both of the parameters of the distribution must be estimated from the data. Slight modifications of the calculated statistics are given to enable the points to be used with small samples. Monte Carlo…

基于风险率的两个概率分布的分布无关比较AI 解读

S-UMMARY Let F(x) and G(x) be the absolutely continuous distribution functions of two life distributions with rF(x) and rG(x) as their respective hazard rates. In the class of increasing failure rate distributions, one-sided scale as well as one-sided location alternatives imply that one hazard rate is uniformly smaller than the other. A new distribution-free test for testing Ho: rF(x) = rG(x) against HA: rF(x) < rG(x) has been proposed. The test is seen to possess robust…

配对比较中的处理对比：大样本结果、应用与若干最优设计AI 解读

Treatment contrasts in paired comparison experiments are considered. Given that specified orthonormal treatment contrasts are null, remaining treatment parameters, orthonormal contrasts among them, and their logarithms are estimated. The estimators are shown to be consistent and, when suitably scaled and centered, to have distribution functions that are normal in the limit for large sample sizes. Hypothesis tests on treatment contrasts are obtained. The limiting distribution…

基于最大 k 个观测值的参数与极高分位数估计AI 解读

We consider an estimation problem when only the k largest observations of a sample of size n are available. It is assumed that the underlying distribution function F belongs to the domain of attraction of a known extreme-value distribution and that k remains fixed as n → ∞. We present estimators for the location and scale parameters and for p-quantiles of F, where p is of the form 1 — c/n (c fixed). These estimators are either asymptotically maximum likelihood or minimum…