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Maximum likelihood paired-comparison ranking and quadratic assignment

最大似然成对比较排序与二次指派

A connexion is identified between maximum likelihood paired-comparison ranking and the problem of quadratic assignment discussed in the operational research literature. This relationship immediately gives a set of computational techniques for obtaining the necessary rankings, and, in addition, provides a general framework for testing the reasonableness of particular object sequencings suggested a priori.

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Estimation of the Distribution Function of a Continuous Type Random Variable through Randomized Response

通过随机化回答估计连续型随机变量的分布函数

In 1965 Stanley Warner [8] illustrated a technique whereby one could estimate from a sample the proportion of persons in a population possessing some characteristic X, without pointedly asking the question, “Do you possess characteristic X?”. The present article uses a variation of these ideas suggested by Warner in a later paper [7] to estimate the distribution function of a continuous-type random variable. The technique is illustrated by estimating an income distribution…

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Bivariate Probit Analysis: Minimum Chi-Square Methods

双变量 Probit 分析:最小卡方方法

In this article we propose two minimum chi-square estimators for a bivariate probit model. We call one estimator the Full Information and the other Limited Information Minimum Chi-Square because the first takes account of all the a priori information while the second does not. Both estimators are shown to be consistent. Moreover, the first is shown to be asymptotically as efficient as the maximum likelihood estimator and yet is computationally much simpler. For illustration,…

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A Convenient Descriptive Model of Income Distribution: The Gamma Density

收入分布的便捷描述模型:伽马密度

The distribution of personal income is approximated by a two-parameter gamma density function (Pearson Type III). The two parameters may be considered as indicators of scale and of inequality, respectively. Maximum likelihood estimates of the parameters are derived from a random sample using graphical techniques, and a likelihood ratio test for the hypothesis that the inequality parameter is the same for different distributions is presented. The derivation of both the…

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On Sample Quantiles from a Regularly Varying Distribution Function

正则变化分布函数下的样本分位数

A law of the iterated logarithm is proved for sample $p$-quantiles when the probability distribution function varies regularly at $\\xi$ with $F(\\xi) = p$.

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An Asymptotic Expansion of the Distribution of the Limited Information Maximum Likelihood Estimate of a Coefficient in a Simultaneous Equation System

联立方程系统中系数的有限信息最大似然估计分布的渐近展开

An asymptotic expansion is made of the distribution of the limited information maximum likelihood estimate of the coefficient of one endogenous variable in an equation with two endogenous variables when the coefficient of the other endogenous variable is prescribed to be unity. The equation is one of a system of simultaneous equations, and all the predetermined variables in the system are assumed to be exogenous. The expansion in terms of the noncentrality parameter, which…

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Confidence Sets for Binary Response Models

二元响应模型的置信集合

Inequalities of Hoeffding are employed to obtain a confidence set for an arbitrary parameterized binary response model. Numerical results are demonstrated for a particular set of experimental data.

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On the Existence of the Exact Moments of Three LIML Structural Variance Estimators for the Case of Two Included Endogenous Variables

含两个内生变量时三种 LIML 结构误差方差估计量精确矩的存在性

This article derives the exact finite sample density functions of three alternative LIML estimators of the variance of the error term in a structural equation containing two endogenous (GΔ = 2) variables contained in a system of G(G ≥ 2) nondynamic structural equations. For the case considered, none of the density functions of the three LIML structural variance estimators define finite moments of positive integer order. It is also demonstrated that, corresponding to a fixed…

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Locally Asymptotically Most Stringent Tests for Paired Comparison Experiments

成对比较实验的局部渐近最严格检验

Following the results of Bhat and Nagnur [2], the locally asymptotically most stringent test of the hypothesis of no preference in paired comparison experiments is derived for the models of Rao and Kupper [9] and Davidson [3]. It is shown that the asymptotic relative efficiency of these tests when compared to the test based on the likelihood ratio statistic is unity.

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Confidence Sets for Binary Response Models

二元响应模型的置信集

Inequalities of Hoeffding are employed to obtain a confidence set for an arbitrary parameterized binary response model. Numerical results are demonstrated for a particular set of experimental data.

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On the Existence of the Exact Moments of Three LIML Structural Variance Estimators for the Case of Two Included Endogenous Variables

含两个内生变量时三种 LIML 结构方差估计量精确矩的存在性

This article derives the exact finite sample density functions of three alternative LIML estimators of the variance of the error term in a structural equation containing two endogenous (GΔ = 2) variables contained in a system of G(G ≥ 2) nondynamic structural equations. For the case considered, none of the density functions of the three LIML structural variance estimators define finite moments of positive integer order. It is also demonstrated that, corresponding to a fixed…

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Locally Asymptotically Most Stringent Tests for Paired Comparison Experiments

成对比较试验的局部渐近最严检验

Following the results of Bhat and Nagnur [2], the locally asymptotically most stringent test of the hypothesis of no preference in paired comparison experiments is derived for the models of Rao and Kupper [9] and Davidson [3]. It is shown that the asymptotic relative efficiency of these tests when compared to the test based on the likelihood ratio statistic is unity.

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Post Data Model Evaluation

JHE PURPOSE of this article is to bring to the attention of the readers of this journal a number of related and important estimators that are currently being discussed in the statistical literature which have implications for applied work since rules are employed which seek to improve the performance of conventional estimators. In spite of the rapid advances, over the last three decades, of economic theory, econometric procedures, and data relating to economic processes and…

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Empirical Probability Plots and Statistical Inference for Nonlinear Models in the Two-Sample Case

两样本非线性模型的经验概率图与统计推断

Let $X$ and $Y$ be two random variables with continuous distribution functions $F$ and $G$ and means $\mu$ and $\xi$. In a linear model, the crucial property of the contrast $\Delta = \xi - \mu$ is that $X + \Delta =_\mathscr{L} Y$, where $= _\mathscr{L}$ denotes equality in law. When the linear model does not hold, there is no real number $\Delta$ such that $X + \Delta = _\mathscr{L} Y$. However, it is shown that if parameters are allowed to be function valued, there is…

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Survivorship Analysis of Heart Transplant Data

心脏移植数据的生存分析

This article presents a number of parametric and nonparametric approaches to the analysis of nonexperimental heart transplant data from the Stanford Heart Transplantation Program, and attempts to come to some conclusion regarding whether heart transplantation is life-extending.

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Methods of Estimation for Markets in Disequilibrium: A Further Study

非均衡市场的估计方法:进一步研究

This paper is concerned with the problem of estimating demand and supply schedules in disequilibrium markets. The results of Fair and Jaffee are expanded in three ways. (1) Their directional method I is modified to yield consistent estimates. (2) A maximum likelihood alternative to their quantitative method is proposed. (3) The price equation is generalized to be a multivariate, stochastic function, and a method is proposed for estimating demand and supply schedules in this…

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A Metric Structure Derived from Subjective Judgments: Scaling Under Perfect and Imperfect Discrimination

从主观判断导出度量结构:完全与不完全辨别下的尺度构建

Assume that to each pair (x, y) of elements of the set A there corresponds probability p(x, y) that y will be chosen as having more of a certain attribute, if the pair (x, y) is presented to the subject. It is shown that if the p(x, y) satisfy a certain set of (logically independent) conditions, then there exists an (essentially unique) measure f of the attribute of elements of A, such that probabilities p(x, y) depend only on differences between f(x) and f(y).

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Estimation and Prediction from Aggregate Data when Aggregates are Measured More Accurately than Their Components

THE CLASSIC PAPER by Grunfeld and Griliches [3] contains many instructive insights into question of circumstances under which an aggregate dependent variable may be forecasted more precisely with a model based on aggregate variables as opposed to an aggregate of forecasts from individual equations. The statistical model they employ is standard regression framework, a single at macro level and a set of seemingly unrelated regressions (to use Zellner's term) at level. Under…

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