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Simultaneous Confidence Bands for Percentile Lines in the General Linear Model

一般线性模型中百分位数线的同时置信带

This article is a generalization of the procedures developed by Steinhorst and Bowden (1971) for constructing confidence bands for the 100βth percentiles in the general linear model. Since the original procedure built these bands about a biased estimator of the 100βth precentile line, some other estimators were tried. While some improvement was noted, the results are not conclusive, suggesting that the best procedure has not been found yet.

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Wald's Test as Applied to Hypotheses in Logit Analysis

Logit 分析中假设检验的 Wald 检验异常

For tests of a single parameter in the binomial logit model, Wald's test is shown to behave in an aberrant manner. In particular, the test statistic decreases to zero as the distance between the parameter estimate and null value increases, and the power of the test, based on its large-sample distribution, decreases to the significance level for alternatives sufficiently far from the null value.

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Elasticities of Substitution among Capital and Occupations in U.S. Manufacturing

美国制造业资本与职业类别之间的替代弹性

This article presents estimates of the elasticities of substitution among capital and up to 12 sex-occupation categories of labor, as well as each input's elasticity of demand, for 12 U.S. manufacturing industries in 1960. These values are derived from a cross-section production function model using states as observations, estimated with data from the Censuses of Manufacturing and Population. The estimator is a nonlinear iterative Zellner procedure, which produces…

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Measuring and Testing Relative Advertising Effectiveness with Split-Cable TV Panel Data

利用分线有线电视面板数据衡量和检验广告相对效果

Various methods of estimating and testing the relative effectiveness of advertising campaigns using split-cable TV consumer panel data are examined. Sensitivities of the methods to missing observations, serial correlation, and the pattern of the expected advertising campaign impact over time are considered. The maximum likelihood estimators for both the case of no missing observations and the missing-observations case are derived, and a nonlinear model which allows for a…

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A Bayesian Data Analysis System for the Evaluation of Social Programs

用于社会项目评估的贝叶斯数据分析系统

The evaluation of social programs is typically hampered by serious methodological problems. Adopting the approach of Bayesian simultaneous estimation proposed by Lindley and Smith (1972) and operationally developed by Jackson, Novick, and Thayer (1971), Novick, Lewis, and Jackson (1973), and Lewis, Wang, and Novick (1975), we demonstrate how some of these problems can be avoided or solved. To accomplish this, we extend the operational method to marginal m-group mean analysis…

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Estimation of Linear Models with Time and Cross-Sectionally Varying Coefficients

系数随时间与截面变化的线性模型估计

In an earlier article (Swamy and Mehta 1975), we formulated a particular decomposition for the coefficient vector in a relationship to be estimated from a time series of cross sections. Specifically, we expressed the coefficient vector as the sum of a common mean vector and two random vectors. One of these random vectors differs among individuals both at a point in time and through time, while the other differs among individuals only. In this article, we state some…

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On the Relation between Change and Initial Value

变化率与初始值之间的关系

Given a series of consecutive measurements on a random sample of individuals, it is often of interest to investigate whether there exists a relationship between the rate of change and the initial value. Assuming that the observations deviate in a random manner from the true values, straightforward regression computations will yield biased results. It is shown that, in the case of the normal distribution, the maximum likelihood (ML) estimates of the second-order moments of…

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The Structure of Technology Over Time: A Model for Testing the "Putty-Clay" Hypothesis

生产技术的跨期结构:检验 putty-clay 假说的模型

This paper develops an econometric model of production technology in terms of the ante-ex description of production possibilities. Ex ante and ex post substitution characteristics are allowed to differ from one another and parametric representations are derived which provide arbitrary second-order approximations to the true underlying characteristics. Nested in the maintained model are the specialized putty-putty, puttyclay, and structures of technology; and hypothesis tests…

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The Estimation of Choice Probabilities from Choice Based Samples

基于选择结果抽样的选择概率估计

Ti-H CONCERN of this paper is the estimation of the parameters of a probabilistic choice model when choices rather than decision makers are sampled. Existing estimation methods presuppose an exogeneous sampling process, that is one in which a sequence of decision makers are drawn and their choice behaviors observed. In contrast, in choice based sampling processes, a sequence of chosen alternatives are drawn and the characteristics of the decision makers selecting those…

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Weighted Least-Squares Analysis of Several Univariate Bradley-Terry Models

若干单变量 Bradley–Terry 模型的加权最小二乘分析

The approach of Grizzle, Starmer, and Koch (1969) to analyzing categorical data using linear and loglinear transformations is applied to the analysis of univariate paired and triple comparison experiments. This method of analysis produces noniterative weighted least-squares estimates of the preference ratings corresponding to the treatments under test and allows for testing hypotheses relative to their values within the framework of the general linear hypothesis. Further,…

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Weighted Least-Squares Analysis of Several Univariate Bradley-Terry Models

若干单变量 Bradley–Terry 模型的加权最小二乘分析

The approach of Grizzle, Starmer, and Koch (1969) to analyzing categorical data using linear and loglinear transformations is applied to the analysis of univariate paired and triple comparison experiments. This method of analysis produces noniterative weighted least-squares estimates of the preference ratings corresponding to the treatments under test and allows for testing hypotheses relative to their values within the framework of the general linear hypothesis. Further,…

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Pooled Time-Series Cross-Section Estimation

时间序列与截面数据的合并估计

PROGRAMS ARE AVAILABLE to facilitate calculation of least squares and instrumental variable coefficients and related statistics from data consisting of time-series observations for each of several cross-sectional units.' The (FORTRAN) programs2 must be used with the SPEAKEASY/FEDEASY processor3 and take the form of three FEDEASY commands that (1) form a moment (cross product) matrix from an arbitrarily large number of observations (CPMATRIX), (2) calculate least squares and…

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A Location Estimator Based on a $U$-Statistic

基于 U 统计量的位置估计量

Let $X_1, \cdots, X_n$ be i.i.d. $F$, and estimate the median of $F$ by the median $T_\beta$ of $\beta X_i + (1 - \beta)X_j, i \neq j$, where $\beta$ is a fixed positive constant. Then $T_\beta$ is the solution of a $U$-statistic equation from which its asymptotic normality is readily derived. The asymptotic relative efficiency of $T_\beta$ is computed for a few cdfs $F$ and seen to be reasonably high for unintuitive choices such as $\beta = .9, \beta = 2$, and also to be…

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Consistent Nonparametric Regression

一致的非参数回归

Let $(X, Y)$ be a pair of random variables such that $X$ is $\mathbb{R}^d$-valued and $Y$ is $\mathbb{R}^{d'}$-valued. Given a random sample $(X_1, Y_1), \cdots, (X_n, Y_n)$ from the distribution of $(X, Y)$, the conditional distribution $P^Y(\bullet \mid X)$ of $Y$ given $X$ can be estimated nonparametrically by $\hat{P}_n^Y(A \mid X) = \sum^n_1 W_{ni}(X)I_A(Y_i)$, where the weight function $W_n$ is of the form $W_{ni}(X) = W_{ni}(X, X_1, \cdots, X_n), 1 \leqq i \leqq n$.…

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Fertility, Schooling, and the Economic Contribution of Children of Rural India: An Econometric Analysis

印度农村的生育、教育与儿童经济贡献:计量分析

A household time-allocative model which explicitly takes into account the economic contribution of children in agricultural areas of less-developed countries is applied to direct-level data pertaining to the rural population of India. Joint family decisions concerning fertility and the allocation of male and female child time to schooling and work activities are examined empirically in a simultaneous equations system. The properties of the formal model are used to derive…

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Measurement Errors in the Estimation of Home Value

房屋价值估计中的测量误差

Home value plays an important role in a variety of fields of research. In this paper, three commonly used measures of home value are evaluated and compared using a framework developed by Jöreskog and Goldberger (1975) for estimation of causal models containing unobserved variables. The paper extends ideas presented by Kain and Quigley (1972) and Kish and Lansing (1954).

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The Precision of Different Experimental Designs for a Random Field

随机场中不同实验设计的精度

Various experimental designs can be used to study the effects of several treatments on a field. The variation of yield in the field will be represented by a realization of a stationary process with isotropic covariance. The variance of an estimator of a treatment effect can be divided into two parts, the first part due to experimental errors and the second part involving the process as well as randomization. This second component will be studied in order to find an optimal…

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Applications of Lorenz Curves in Economic Analysis

洛伦兹曲线在经济分析中的应用

The Lorenz curve relates the cumulative proportion of income units to the cumulative proportion of income received when units are arranged in ascending order of their income. In the past the curve has been mainly used as a convenient graphic device to represent the size distribution of income and wealth. In this paper the Lorenz curve technique is used as a tool to introduce distributional considerations in economic analysis. The concept has been extended and generalized to…

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Two-Stage Least Squares: In Which Direction Should the Residuals Be Minimized?

两阶段最小二乘:应沿哪个方向最小化残差?

A structural equation in a complete system may be written with the coefficient of one endogenous variable as unity and the coefficients of the other endogenous variables as parameters. To estimate these parameters two-stage least squares is usually applied by minimizing residuals in the direction of the first variable. In this paper, when there is one such parameter, that procedure is compared with adapting two-stage least squares to minimize residuals in the direction of…

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