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Composite Estimation in Finite Populations

It is common practice in large recurring surveys to employ rotation sampling schemes. Composite estimators are often used in association with rotation schemes to reduce the variability of the survey estimators. In this article, expressions for the variances of certain composite estimators are derived. It is demonstrated how the variance expressions may be used in planning panel surveys and in certain time series analyses. This work is illustrated by the Census Bureau's…

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Some Useful Representations for Constrained Mixed-Model Estimation

约束混合模型估计的若干实用表示

Mixed-model computations can be accomplished efficiently by using the Henderson mixed-model equations. An augmented version of the equations is developed for the case where there are constraints on the fixed effects. Equations comparable to the conjugate normal equations are also developed. These equations are useful for direct computation and, in the case of patterned designs, lend themselves well to algebraic simplification.

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Some Useful Representations for Constrained Mixed-Model Estimation

约束混合模型估计的若干实用表示

Mixed-model computations can be accomplished efficiently by using the Henderson mixed-model equations. An augmented version of the equations is developed for the case where there are constraints on the fixed effects. Equations comparable to the conjugate normal equations are also developed. These equations are useful for direct computation and, in the case of patterned designs, lend themselves well to algebraic simplification.

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A Generalized Compound Poisson Model for Consumer Purchase Panel Data Analysis

消费者购买面板数据分析的广义复合泊松模型

A compound Poisson distribution, the Ehrenberg NBD model, has proven useful in the past for analyzing consumer purchase behavior encountered in dealing with frequently purchased low-cost consumer items. The present article proposes the use of a generalized negative binomial distribution in which the NBD model is used as a purchase occasion component and is combined explicitly with the conditional distributions of the single-purchase volume variables associated with the…

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Specification Tests in Econometrics

计量经济学中的模型设定检验

Using the result that under the null hypothesis of no misspecification an asymptotically efficient estimator must have zero asymptotic covariance with its difference from a consistent but asymptotically inefficient estimator, specification tests are devised for a number of model specifications in econometrics. Local power is calculated for small departures from the null hypothesis. An instrumental variable test as well as tests for a time series cross section model and the…

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Dynamic Aspects of Earning Mobility

收入流动的动态方面

Abs tract This paper proposes an econometric methodology to deal with life cycle earnings and mobility among discrete earnings classes. First, we use panel data on male log earnings to estimate an earnings function with permanent and serially correlated transitory components due to both measured and unmeasured variables. Assuming that the error components are normally distributed, we develop statements for the probability that an individual's earnings will fall into a…

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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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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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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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Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

方差分量估计及相关问题的极大似然方法

Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be…

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Estimation of Time-Varying Markov Processes with Aggregate Data

利用汇总数据估计时变马尔可夫过程

The exact stochastic character of observed data from a Markov process is derived for the case where only aggregate stocks, as opposed to individual transitions, are observed. Particular attention is devoted to the distinction between data generated by a panel study, where a single group of individuals is followed over time, and that generated by random sampling, where the observed groups are not identical over time. Several alternative estimators are developed which take…

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A Purchase Incidence Model with Inverse Gaussian Interpurchase Times

购买间隔服从逆高斯分布的购买发生模型

This paper deals with a new purchase incidence model where the interpurchase time of an individual household is described by a two-parameter inverse Gaussian distribution, and the population heterogeneity is modeled by the natural conjugate family which has truncated t and modified gamma marginals. The model, more flexible than the exponential and one-parameter gamma models previously used for purchase incidence, is applied to consumer panel data on toothpaste purchases and…

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An Investigation of the F -Test Procedure as an Estimation Short-Cut

作为估计捷径的F检验程序研究

Summary When estimating fixed effects in the one-way anova model the F-test for the equality of the group means is sometimes used as a preliminary test of significance. This paper provides alternatives to the percentage points in the F-test by re-formulating the problem under estimation, as opposed to hypothesis testing, criteria. The new procedure possesses strikingly different properties, and it is argued that fixed-size tests are not obviously relevant within an…

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Extension of the Gauss-Markov Theorem to Include the Estimation of Random Effects

将随机效应估计纳入 Gauss–Markov 定理的扩展

The general mixed linear model can be written $y = X\alpha + Zb$, where $\alpha$ is a vector of fixed effects and $b$ is a vector of random variables. Assume that $E(b) = 0$ and that $\operatorname{Var} (b) = \sigma^2D$ with $D$ known. Consider the estimation of $\lambda_1'\alpha + \lambda_2'\beta$, where $\lambda_1'\alpha$ is estimable and $\beta$ is the realized, though unobservable, value of $b$. Among linear estimators $c + r'y$ having $E(c + r'y) \equiv E(\lambda_1'\alpha + \lambda_2'b)$…

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Autoregressive and Nonautoregressive Elements in Cross-Section Forecasts of Inflation

通胀横截面预测中的自回归与非自回归成分

Using cross-section data collected from a panel of institutional investors in 1969, 1970, 1972, this paper focuses on how knowledgeable individuals formulate forecasts of future rates of price inflation, We estimate return-to-normality and error-learning forecasting models and inquire whether such equations can be interpreted simply as reduced forms of an autoregressive forecasting structure. Assuming that respondents' expectations were formed rationally in the sense of…

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An Extension of the T -Method to General Unbalanced Models of Fixed Effects

将 T 方法扩展至一般非平衡固定效应模型

1. Introduction and Summary Among the various procedures for simultaneous interval estimation, Tukey's T-method gives the shortest confidence intervals for pairwise contrasts when it is applicable. (Cf. Scheffé, 1959, Ch. 3; Miller, 1966, Ch. 2.) However, the T-method in its exact formulation (excluding one way anova, see Spjøtvoll and Stoline, 1973) is restricted to well-balanced designs. In this paper we discuss a generalized T-type procedure for simultaneous interval…

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Bayesian Analysis of Error Components Regression Models

误差分量回归模型的贝叶斯分析

This article examines the use of a two-way, random-effects, model with correlated errors and additional explanatory variables in combining cross-section with time series data. This model has been analyzed from a Bayesian viewpoint. Methods are developed for computing posterior distributions of slope coefficients. The advantage of our approach over sampling theory approaches is briefly discussed. It has been shown how one can obtain reasonable inferences about slope…

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Bayesian Analysis of Error Components Regression Models

误差分量回归模型的贝叶斯分析

This article examines the use of a two-way, random-effects, model with correlated errors and additional explanatory variables in combining cross-section with time series data. This model has been analyzed from a Bayesian viewpoint. Methods are developed for computing posterior distributions of slope coefficients. The advantage of our approach over sampling theory approaches is briefly discussed. It has been shown how one can obtain reasonable inferences about slope…

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Linear regression with randomly dispersed parameters

参数随机分散的线性回归

Consider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over successive observations on that individual. Maximum likelihood estimators of the mean and dispersion of the parameters and of the disturbance variance are derived. These estimators yield empirical Bayes estimators of the individual parameter veotors. The properties of the estimators are…

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Linear Regression with Randomly Dispersed Parameters

参数随机分散的线性回归

Consider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over successive observations on that individual. Maximum likelihood estimators of the mean and dispersion of the parameters and of the disturbance variance are derived. These estimators yield empirical Bayes estimators of the individual parameter veotors. The properties of the estimators are…

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