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A note on the estimation of a distribution function and quantiles by a kernel method

用核方法估计分布函数与分位数的札记

A distribution function is estimated by integrating a kernel estimator of the density. Quantiles are estimated by inverting the estimate of the distribution function. Second-order properties of both these estimators are studied.

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Trimmed Least Squares Estimation in the Linear Model

线性模型中的修剪最小二乘估计

We consider two methods of defining a regression analog to a trimmed mean. The first was suggested by Koenker and Bassett and uses their concept of regression quantiles. Its asymptotic behavior is completely analogous to that of a trimmed mean. The second method uses residuals from a preliminary estimator. Its asymptotic behavior depends heavily on the preliminary estimate; it behaves, in general, quite differently than the estimator proposed by Koenker and Bassett, and it…

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Estimating the Population Median by Nomination Sampling

通过提名抽样估计总体中位数

In nomination sampling, the largest values from several independent random samples (nominees) are rank ordered, and an estimate of the population median is formed by interpolating between 2 of these order statistics. The resulting estimate compares favorably to the sample median of a simple random sample from the same population. When historical data sets retain only extreme values, nomination sampling may offer the only practical way to estimate the population median. The…

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Simultaneous Confidence Bounds for the Tail of an Inverse Distribution Function

逆分布函数尾部的同时置信界

Confidence bounds are derived for the upper 100$p$ percentile of an inverse distribution function. These bounds are considerably less conservative than similar bounds which apply to the entire function.

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Asymptotic Expansions of the Distributions of Estimators in a Linear Functional Relationship and Simultaneous Equations

线性函数关系与联立方程中估计量分布的渐近展开

We derive asymptotic expansions of the distributions of the maximum likelihood (ML) estimator and the ordinary least squares (OLS) estimator in a linear functional relationship model as the sample size increases infinitely. These expansions are equivalent to the asymptotic expansions of the distributions of the limited information maximum likelihood (LIML) estimator when the covariance is known to within a proportionality constant and the two-stage least squares (TSLS)…

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Identification of the Ordered Bivariate Normal Distribution by Minimum Variate

通过最小值变量识别有序二元正态分布

For full-rank covariance matrix and other subfamilies of the ordered bivariate normal distribution, the identifiability of parameters by the minimum variate is demonstrated. For the general family, the distribution is not identified. These identifiability questions arise in connection with estimation within certain econometric models, for example, Tobin and Fair-Jaffee.

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Inferential Procedures in Stable Distributions for Class Frequency Data on Incomes

分组收入频数数据下稳定分布的统计推断

This paper discusses inferential procedures for the family of stable distributions, when the data are tabulated in the form of interval frequencies. The estimation criteria used are minimum chi-square and multinomial maximum likelihood. In evaluating the theoretical probabilities corresponding to the intervals, use is made of the inversion theorem for characteristic functions. Chi-square tail probabilities for independent samples are pooled by means of theKolmogorov…

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Distributions of Some One-Sided k -Sample Smirnov-Type Statistics

若干单侧多样本Smirnov型统计量的分布

Consider the problem of testing the equality of k populations in cases in which the populations can be ordered a priori from low to high on the basis of some underlying variable. This article proposes a new statistic based on the sums of the Smirnov-type statistic and provides evidence that the test based on this statistic has high power for a wide range of alternatives suggested by this problem. To construct the statistic, let Fj (x) be the empirical distribution for the…

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Analyzing Social Networks as Stochastic Processes

将社会网络作为随机过程分析

This article presents a new methodology for studying a social network of interpersonal relationships, based on stochastic modeling of the changes that occur in the network over time. Specifically, we postulate that these changes can be modeled as a continuous-time Markov chain. The transition rates for the chain are dependent on a small set of parameters that measure the importance of various aspects of social structure on the probability of change. We discuss the…

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The $n^{-2}$-Order Mean Squared Errors of the Maximum Likelihood and the Minimum Logit Chi-Square Estimator

最大似然与最小Logit卡方估计量的n⁻²阶均方误差

The $n^{-2}$ order mean squared errors of the maximum likelihood and the minimum chi-square estimator of the logit regression model are derived and the latter is shown to be superior for many parameter values considered. The maximum likelihood is shown to be better if the bias of each estimator is corrected to the order of $n^{-1}$; however, the difference is shown to be negligibly small in many practical situations.

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Formulation and Statistical Analysis of the Mixed, Continuous/Discrete Dependent Variable Model in Classical Production Theory

经典生产理论中连续与离散混合因变量模型的构建与统计分析

Data sets which contain jointly endogenous discrete and continuous variables often occur in practice. This paper presents a model of the economic and stochastic processes generating such data as well as methods of estimation. A maximum likelihood estimator is examined and found to exhibit the usual optimality but it is computationally burdensome. A simpler estimator, the QREG, which is a simple weighted average of separate probit (or logit) and regression estimates is…

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Improving the Maximum Likelihood Estimate in Linear Functional Relationships for Alternative Parameter Sequences

不同参数序列下线性函数关系最大似然估计的改进

We propose an improvement of the maximum likelihood (ML) estimate in linear functional relationships. The improved estimate is a linear combination of the ML and the least squares estimate so as to remove the bias of the former. Approximations to the distribution of the estimate are derived for two alternative parameter sequences: a sequence in which the noncentrality parameter (the spread of the true values) increases while the number of observations stays fixed, and that…

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A Monte Carlo Study of Small-Sample Properties of Simultaneous Equation Estimators with Normal and Nonnormal Disturbances

正态与非正态扰动下联立方程估计量的小样本蒙特卡洛比较

In this paper we consider four alternative forms of two-parameter normal and nonnormal error distributions and report on a Monte Carlo study of the small-sample properties of least squares, two-stage least squares, three-stage least squares and full information maximum likelihood estimators. On the basis of 1,000 replications of sample size 20 in two experiments on an overidentified model, we found that the small-sample rankings of econometric estimators of both structural…

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Asymptotic Covariance Matrices of Two-Stage Probit and Two-Stage Tobit Methods for Simultaneous Equations Models with Selectivity

含选择机制的联立方程模型中两阶段 Probit 与 Tobit 方法的渐近协方差矩阵

Lung-Fei Lee, G. S. Maddala, R. P. Trost, Asymptotic Covariance Matrices of Two-Stage Probit and Two-Stage Tobit Methods for Simultaneous Equations Models with Selectivity, Econometrica, Vol. 48, No. 2 (Mar., 1980), pp. 491-503

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Estimation of Quantiles in Certain Nonparametric Models

某些非参数模型中的分位数估计

The deficiency of sample quantiles with respect to quasiquantiles is investigated under the assumption that the true density function has bounded derivatives. Then the sample quantile is still an efficient estimator of the true quantile but the relative deficiency of sample quantiles with respect to suitably defined quasiquantiles quickly tends to infinity for increasing sample sizes. If the second derivative of the true density function is bounded, then adaptive estimators…

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The Estimation of the Prais-Houthakker Model of Equivalence Scales

Prais–Houthakker 家庭等价尺度模型的估计

Given a preference basis for the model, a household's general equivalence scale is seen to be a cost of living index relative to the reference household type defined at constant prices. A maximum likelihood estimation procedure which can be applied both to cross-section data and pooled time-series/cross-sections is derived. The lack of identification of the model is established theoretically and checked empirically on British family expenditure survey data. With prior…

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Disequilibrium Econometrics in Simultaneous Equations Systems

联立方程系统中的非均衡计量经济学

This paper considers the econometric problems raised by multi-market disequilibrium models. It uses a specification which is derived from general disequilibrium theory and, therefore, provides a first bridge between the economic theory approach and the econometric theory approach of disequilibrium. The model is piecewise linear; the problem of the existence of a reduced form, which is a crucial issue in nonlinear models, is solved. Limited information estimators as well as…

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