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Model misspecification in proportional hazards regression

比例风险回归中的模型误设

The proportional hazards model is frequently used to evaluate the effect of treatment on failure time events in randomised clinical trials. Concomitant variables are usually available and may be considered for use in the primary analyses under the assumption that incorporating them may reduce bias or improve efficiency. In this paper we consider two approaches to including covariate information: regression modelling and stratification. We focus on the setting where covariate…

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Testing Ordered Alternatives in the Presence of Incomplete Data

不完整数据下的有序备择检验

In testing the null hypothesis of no treatment effects in a randomized block experiment, a researcher may restrict attention to an ordered alternative and thereby increase the power of his test. Jonckheere and later Page proposed such test statistics based on the Kendall and Spearman correlation coefficients. Motivated by notions of distance between permutations, we generalize Jonckheere's and Page's tests to the situation in which one or more observations are missing from…

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Nonparametric Methods for Stratified Two-Sample Designs with Application to Multiclinic Trials

分层两样本设计的非参数方法及多中心临床试验应用

Motivated by some problems arising from multiclinic trials, we consider stratified two-sample designs. Nonparametric effects are defined and nonparametric hypotheses are formulated in a design where treatment, centers (strata), and interactions are assumed to be fixed factors. The interpretation of the nonparametric effects and hypotheses is analyzed in two classes of semiparametric models: the linear models and models with Lehmann alternatives. The case where centers and…

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Approximations to Multivariate Normal Rectangle Probabilities Based on Conditional Expectations

基于条件期望的多元正态矩形区域概率近似

Two new approximations for multivariate normal probabilities for rectangular regions, based on conditional expectations and regression with binary variables, are proposed. One is a second-order approximation that is much more accurate but also more numerically time-consuming than the first-order approximation. A third approximation, based on the moment-generating function of a truncated multivariate normal distribution, is proposed for orthant probabilities only. Its…

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Testing Ordered Alternatives in the Presence of Incomplete Data

不完整数据下有序备择假设的检验

In testing the null hypothesis of no treatment effects in a randomized block experiment, a researcher may restrict attention to an ordered alternative and thereby increase the power of his test. Jonckheere and later Page proposed such test statistics based on the Kendall and Spearman correlation coefficients. Motivated by notions of distance between permutations, we generalize Jonckheere's and Page's tests to the situation in which one or more observations are missing from…

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A Note on the Bias due to Omitted Confounders

关于遗漏混杂因素所致偏差的札记

In observational studies some confounders may be unknown and therefore omitted from the analysis while others are adjusted for. Approximations to the functions defining the relationship between the parameters in the full and reduced models are proposed leading to asymptotic bias estimates. Numerical calculations for logistic and Poisson regression models show good agreement between asymptotic and simulation bias. A data set containing the relationship between low birth…

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Revisiting the Sen Poverty Index

再论森贫困指数

A modification of the official Sen poverty index yields an index which is not only continous in individual incomes and consistent with the transfer axiom, but also admits a geometric interpretation in terms of the area beneath a graph called the inverse generalized Lorenz curve for normalized poverty gaps by Jenkins and Lambert (1993) or the poverty gap profile by Shorrocks (1994).

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Prediction Functions for Categorical Panel Data

分类面板数据的预测函数

Prediction of categorical responses in panel studies is considered. Prediction functions based on general conditional $\log$-linear models are investigated for statistical properties both from a population perspective and a sampling perspective. Problems such as existence and uniqueness of optimal prediction functions are addressed, and basic properties of measures of prediction quality are examined. Estimation, consistency and asymptotic normality are studied for the…

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Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study

分位数回归模型渐近协方差矩阵估计的蒙特卡洛研究

This Monte Carlo study examines several estimation procedures of the asymptotic covariance matrix in the quantile and censored quantile regression models: design matrix bootstrap, error bootstrapping, order statistic, sigma bootstrap, homoskedastic kernel, and heteroskedastic kernel. The Monte Carlo samples are drawn from two alternative data sets: (a) the unaltered Current Population Survey (CPS) for 1987 and (b) this CPS data with independence between error term and…

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Analytical Score Function for Irregularly Sampled Continuous Time Stochastic Processes with Control Variables and Missing Values

不规则采样、控制变量与缺失值下连续时间随机过程的解析得分函数

The unknown structural parameters of a continuous/discrete state space model are estimated by maximum likelihood in the presence of irregular sampling, missing values, and cross-sections of time series (panel data). Exogenous (control) variables are included, and the sampling scheme and missing data pattern can be different for each variable and system. Furthermore, the derived non-linear optimization algorithm with analytical score function can be used for the discrete time…

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Another look at the instrumental variable estimation of error-components models

重新审视误差分量模型的工具变量估计

This article develops a framework for efficient IV estimators of random effects models with information in levels which can accommodate predetermined variables. Our formulation clarifies the relationship between the existing estimators and the role of transformation in panel data models. We characterise the valid transformations for relevant models and show the optimal estimators are invariant to the transformation used to remove individual effects. We present an alternative…

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Efficient estimation of models for dynamic panel data

动态面板数据模型的有效率估计

In this paper we consider a dynamic model for panel data. We show that, under standard assumptions, there are more moment conditions than are currently exploited in the literature. Some of these are linear, but others are quadratic, so that nonlinear GMM is required. We also show that exogenous regressors generate a larger number of relevant moment conditions in a dynamic model than they would in a static model.

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Econometrics of First-Price Auctions

一价拍卖的计量经济学

This paper proposes a convenient estimation method for the empirical study of auction models. The authors focus on first-price sealed-bid and descending auctions within the private value paradigm. The method relies upon a simulated nonlinear least squares objective function appropriately adjusted. Asymptotic properties are established and some extensions are discussed. The method is applied to a market of agricultural products. The structural modeling takes into account the…

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Automobile Prices in Market Equilibrium

市场均衡中的汽车价格

This paper develops techniques for empirically analyzing demand and supply in differentiated product markets and then applies these techniques to the U.S. automobile industry. The authors' framework enables one to obtain estimates of demand and cost parameters for a class of oligopolistic differentiated products markets. These estimates can be obtained using only widely available product-level and aggregate consumer-level data, and they are consistent with a structural model…

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Measurement Error and Earnings Dynamics: Some Estimates From the PSID Validation Study

测量误差与劳动收入动态:PSID 验证研究中的若干估计

Previous empirical work on measurement error in survey earnings data has shown that the variance of the measurement error is roughly constant over time, it is negatively correlated with true earnings, and it is autocorrelated with previous measurement errors. This paper proposes a simple model where the measurement error stems from underreporting of transitory earnings fluctuations and a white noise component. The model fits well to data from the PSID Validation Study. The…

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Reassessing Brand Loyalty, Price Sensitivity, and Merchandising Effects on Consumer Brand Choice

This paper reports the results of an empirical study of household brand choices over four scanner panel data sets. The study uses a random-effects, autocorrelated logistic regression model. The analysis presents evidence that the brand choice process is not zero-order. In addition, the influence of in-store displays and feature advertisements on switching is shown to be about two to three times more effective than estimates obtained from previous studies. Finally, the…

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Deficiency of the Sample Quantile Estimator with Respect to Kernel Quantile Estimators for Censored Data

删失数据中样本分位数估计相对核分位数估计的样本量亏损

Consider a statistical procedure (Method A) which is based on $n$ observations and a less effective procedure (Method B) which requires a larger number $k_n$ of observations to give equal performance under a certain criterion. To compare two different procedures, Hodges and Lehmann suggested that the difference $k_n - n$, called the deficiency of Method B with respect to Method A, is the most natural quantity to examine. In this article, the performance of two kernel…

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Upper and Lower Bound Distributions That Give Simultaneous Confidence Intervals for Quantiles

用于分位数同时置信区间的上下界分布

We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution…

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Instrumental Variable Estimation in Binary Regression Measurement Error Models

二元回归测量误差模型中的工具变量估计

We describe two approaches to instrumental variable estimation in binary regression measurement error models. The methods entail constructing approximate mean models for the binary response as a function of the measured predictor, the instrument, and any covariates in the model. Estimates are obtained by exploiting relationships between regression parameters, just as in linear instrumental variable estimation. In the course of deriving the approximate mean models, we obtain…

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A Random-Effects Model for Ordered Categorical Data

有序分类数据的随机效应模型

This article presents a random-effects model for multivariate and grouped univariate ordered categorical data. The assumed family of distributions for the random effects adopts a wide variety of forms and shapes. The model's likelihood has a closed expression and can be computed without recourse to numerical integration or Gaussian quadrature. A bivariate and a grouped univariate example are used to illustrate the proposed model.

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Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity

可变处理强度模型中平均因果效应的两阶段最小二乘估计

Two-stage least squares (TSLS) is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted-variables bias in single-equation estimation. We show here that TSLS can also be used to estimate the average causal effect of variable treatments such as drug dosage, hours of exam preparation, cigarette smoking, and years of schooling. The average causal effect in which we are interested is a conditional…

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Problems with Instrumental Variables Estimation when the Correlation between the Instruments and the Endogenous Explanatory Variable is Weak

工具变量与内生解释变量弱相关时的估计问题

We draw attention to two problems associated with the use of instrumental variables (IV), the importance of which for empirical work has not been fully appreciated. First, the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the IV estimates even if only a weak relationship exists between the instruments and the error in the structural equation. Second, in finite samples, IV estimates are…

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Upper and Lower Bound Distributions that Give Simultaneous Confidence Intervals for Quantiles

用于分位数同时置信区间的上下界分布

We propose a new method for constructing parametric confidence intervals for quantiles of an unknown distribution. These confidence intervals are constructed so that the joint probability that all intervals simultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidence limits to define an upper (or lower) bound distribution function, which we call an upper (or lower) tolerance distribution…

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On the Use of a Working Correlation Matrix in Using Generalised Linear Models for Repeated Measures

重复测量广义线性模型中工作相关矩阵的使用问题

In a seminal paper Liang & Zeger (1986) extended the use of generalised linear models to repeated measures data. They based the analysis on specifications for the means and variances of the observations, as usual for generalised linear models, but showed how specifications for the correlations between measurements made on the same unit could be avoided by using a ‘working’ correlation matrix. In some cases the parameters involved in this matrix are subject to an uncertainty…

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