Double bootstrap estimation of variance under systematic sampling with probability proportional to size

Variance estimation under systematic sampling with probability proportional to size is known to be a difficult problem. We attempt to tackle this problem by the bootstrap resampling method. It is shown that the usual way to bootstrap fails to give satisfactory variance estimates. As a remedy, we propose a double bootstrap method which is based on certain working models and involves two levels of resampling. Unlike existing methods which deal exclusively with the Horvitz–Thompson estimator, the double bootstrap method can be used to estimate the variance of any statistic. We illustrate this within the context of both mean and median estimation. Empirical results based on five natural populations are encouraging.     

Performance of a bartlett-type modification for the deviance

Cordeiro (1983) has derived the expected value of the deviance for generalized linear models correct to terms of order n ^-1 being the sample size. Then a Bartlett-type factor is available for correcting the first moment of the deviance and for fitting its distribution. If the model is correct, the deviance is not, in general, distributed as chi-squared even asymptotically and very little is known about the adequacy of the X ² approximation. This paper through simulation studies examines the behaviour of the deviance and a Bartlett adjusted deviance for testing the goodness-of-fit of a generalized linear model. The practical use of such adjustment is illustrated for some gamma and Poisson models. It is suggested that the null distribution of the adjusted deviance is better approximated by chi-square than the distribution of the deviance.     

Two-stage hierarchical modeling for analysis of subpopulations in conditional distributions

In this work, we develop modeling and estimation approach for the analysis of cross-sectional clustered data with multimodal conditional distributions where the main interest is in analysis of subpopulations. It is proposed to model such data in a hierarchical model with conditional distributions viewed as finite mixtures of normal components. With a large number of observations in the lowest level clusters, a two-stage estimation approach is used. In the first stage, the normal mixture parameters in each lowest level cluster are estimated using robust methods. Robust alternatives to the maximum likelihood estimation are used to provide stable results even for data with conditional distributions such that their components may not quite meet normality assumptions. Then the lowest level cluster-specific means and standard deviations are modeled in a mixed effects model in the second stage. A small simulation study was conducted to compare performance of finite normal mixture population parameter estimates based on robust and maximum likelihood estimation in stage 1. The proposed modeling approach is illustrated through the analysis of mice tendon fibril diameters data. Analyses results address genotype differences between corresponding components in the mixtures and demonstrate advantages of robust estimation in stage 1.     

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

This paper uses control variables to identify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance. Here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable. Also, for any control variable, identification results are given for quantile, average, and policy effects. Bounds are given when a common support assumption is not satisfied. Estimators of identified objects and bounds are provided, and a demand analysis empirical example is given.     

Asymptotics for Statistical Treatment Rules

This paper develops asymptotic optimality theory for statistical treatment rules in smooth parametric and semiparametric models. Manski (2000, 2002, 2004) and Dehejia (2005) have argued that the problem of choosing treatments to maximize social welfare is distinct from the point estimation and hypothesis testing problems usually considered in the treatment effects literature, and advocate formal analysis of decision procedures that map empirical data into treatment choices. We develop large‐sample approximations to statistical treatment assignment problems using the limits of experiments framework. We then consider some different loss functions and derive treatment assignment rules that are asymptotically optimal under average and minmax risk criteria.     

Efficiency Bounds for Missing Data Models With Semiparametric Restrictions

This paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random (MAR) coincides with that of a particular augmented moment condition problem. The augmented system consists of the inverse probability weighted (IPW) original moment restriction and an additional conditional moment restriction which exhausts all other implications of the MAR assumption. The paper also investigates the value of additional semiparametric restrictions on the conditional expectation function (CEF) of the original moment function given always observed covariates. In the program evaluation context, for example, such restrictions are implied by semiparametric models for the potential outcome CEFs given baseline covariates. The efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem. Some implications of these results for estimation are briefly discussed.     

The Effect of Expected Income on Individual Migration Decisions

This paper develops a tractable econometric model of optimal migration, focusing on expected income as the main economic influence on migration. The model improves on previous work in two respects: it covers optimal sequences of location decisions (rather than a single once‐for‐all choice) and it allows for many alternative location choices. The model is estimated using panel data from the National Longitudinal Survey of Youth on white males with a high‐school education. Our main conclusion is that interstate migration decisions are influenced to a substantial extent by income prospects. The results suggest that the link between income and migration decisions is driven both by geographic differences in mean wages and by a tendency to move in search of a better locational match when the income realization in the current location is unfavorable.     

价值相关性的实证研究方法评述

本文梳理了价值相关性研究的研究方法及其发展,并对其进行评述。按研究方法分,价值相关性研究分为事件研究法和估值模型法。事件研究法依赖有效市场假说,仅能检验某一事件能否引起市场反应,其对权益价值的具体影响则难以估计,而且短窗口选择存在操作上的困难。估值模型法在实证检验中应用相对较广,然而几乎所有的估值模型都没要考虑期权的影响,而且运用价格模型和收益模型有时得到截然相反的结论。因此,本文认为,今后的研究应重点关注三个方面：第一,继续修正估值模型。第二,抛开相关性和可靠性联合检验的方式,关注会计信息的可靠性。第三,应多角度研究价值相关性,而不仅仅局限于投资者视角。     

关于概率论与数理统计教学的几点体会

随着社会的进步和科学技术的发展,概率统计的思维方式和方法在各个领域越来越受到重视,并被广泛应用。在教学过程中应注意激发学生的学习兴趣;借助多媒体,增加案例教学;加强实践教学,以不断提高教学效果和学生的动手能力。