Inference for functions of parameters in discrete distributions based on fiducial approach: Binomial and Poisson cases

In this article, we propose a simple method of constructing confidence intervals for a function of binomial success probabilities and for a function of Poisson means. The method involves finding an approximate fiducial quantity (FQ) for the parameters of interest. A FQ for a function of several parameters can be obtained by substitution. For the binomial case, the fiducial approach is illustrated for constructing confidence intervals for the relative risk and the ratio of odds. Fiducial inferential procedures are also provided for estimating functions of several Poisson parameters. In particular, fiducial inferential approach is illustrated for interval estimating the ratio of two Poisson means and for a weighted sum of several Poisson means. Simple approximations to the distributions of the FQs are also given for some problems. The merits of the procedures are evaluated by comparing them with those of existing asymptotic methods with respect to coverage probabilities, and in some cases, expected widths. Comparison studies indicate that the fiducial confidence intervals are very satisfactory, and they are comparable or better than some available asymptotic methods. The fiducial method is easy to use and is applicable to find confidence intervals for many commonly used summary indices. Some examples are used to illustrate and compare the results of fiducial approach with those of other available asymptotic methods.     

Estimating and using propensity score in presence of missing background data: an application to assess the impact of childbearing on wellbeing

Propensity score methods are an increasingly popular technique for causal inference. To estimate propensity scores, we must model the distribution of the treatment indicator given a vector of covariates. Much work has been done in the case where the covariates are fully observed. Unfortunately, many large scale and complex surveys, such as longitudinal surveys, suffer from missing covariate values. In this paper, we compare three different approaches and their underlying assumptions of handling missing background data in the estimation and use of propensity scores: a complete-case analysis, a pattern-mixture model based approach developed by Rosenbaum and Rubin (J Am Stat Assoc79:516–524, 1984), and a multiple imputation approach. We apply these methods to assess the impact of childbearing events on individuals’ wellbeing in Indonesia, using a sample of women from the Indonesia Family Life Survey. I am grateful to all the participants at the project “Poverty Dynamics and Fertility in Developing Countries” for their support and encouragement. Special thanks are due to Fabrizia Mealli for her insightful suggestions and discussions. I also thank Jungho Kim, who is the main author of the STATA code to produce Indonesia consumption expenditure. Finally, I thank Arnstein Aassve, and Letizia Mencarini for help working with the data and their very useful discussions, and Alexia Fuernkranz-Prskawetz, and Henriette Engelhardt for detailed comments and suggestions which have improved the paper. Financial support from CNR-EFS and COFIN 2005 is gratefully acknowledged.     

Does social insurance enrollment improve citizen assessment of local government performance? Evidence from China

Although many studies claim that social policies are “carrots” that authoritarian leaders use to garner public support, the assumption that social benefits can boost public support of government has been rarely tested empirically, especially at the local levels. This article investigates the effects of social insurance enrollment on citizens' assessment of local government performance using data from the 2010 China Family Panel Study. We use propensity score matching to reduce selection bias and ordered probit regressions with fixed effects to examine these possible effects. We find that social insurance enrollment had a significant positive effect on rural citizens' assessment of government performance, but this effect did not exist for their urban and migrant peers. This discrepancy could be largely due to the groups' different expectations for government redistribution and their distinct experiences of China's social welfare reform. We conclude that the Chinese authoritarian government has achieved partial success in its attempt to use social policies to maintain popular support.     

A Simple Analysis of the Exact Probability Matching Prior in the Location-Scale Model

It has long been asserted that in univariate location-scale models, when concerned with inference for either the location or scale parameter, the use of the inverse of the scale parameter as a Bayesian prior yields posterior credible sets that have exactly the correct frequentist confidence set interpretation. This claim dates to at least Peers, and has subsequently been noted by various authors, with varying degrees of justification. We present a simple, direct demonstration of the exact matching property of the posterior credible sets derived under use of this prior in the univariate location-scale model. This is done by establishing an equivalence between the conditional frequentist and posterior densities of the pivotal quantities on which conditional frequentist inferences are based.     

Bias-corrected estimators of scalar skew normal

One problem of skew normal model is the difficulty in estimating the shape parameter, for which the maximum likelihood estimate may be infinite when sample size is moderate. The existing estimators suffer from large bias even for moderate size samples. In this article, we proposed five estimators of the shape parameter for a scalar skew normal model, either by bias correction method or by solving a modified score equation. Simulation studies show that except bootstrap estimator, the proposed estimators have smaller bias compared to those estimators in literature for small and moderate samples.     

Objective Bayesian hypothesis testing in regression models with first-order autoregressive residuals

This article considers the objective Bayesian testing in the normal regression models with first-order autoregressive residuals. We propose some solutions based on a Bayesian model selection procedure to this problem where no subjective input is considered. We construct the proper priors for testing the autocorrelation coefficient based on measures of divergence between competing models, which is called the divergence-based (DB) priors and then propose the objective Bayesian decision-theoretic rule, which is called the Bayesian reference criterion (BRC). Finally, we derive the intrinsic test statistic for testing the autocorrelation coefficient. The behavior of the Bayes factor-based DB priors is examined by comparing with the BRC in a simulation study and an example.     

ASYMPTOTIC TESTS FOR GROWTH CURVE MODELS WITH AUTOREGRESSIVE ERRORS

This paper presents the limit distribution (as the number of time points increase) for the score vector of a growth curve model assuming both stationary and explosive autoregressive (A.R.) errors. Limit distributions of the score statistic and the likelihood-ratio statistic for testing composite hypotheses about the regression parameters of several growth curves, when the autocorrelation parameters are treated as nuisance parameters, are presented.     

Dynamic Matching,Two‐Sided Incomplete Information,and Participation Costs: Existence and Convergence to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and, each unit of time, continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and the winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady‐state equilibria that are perfect Bayesian. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show the existence of equilibria for δ sufficiently small, provided the discount rate is small relative to the participation costs.     

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n^−1/2 for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests.     

Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)

We propose a locally efficient estimator for a class of semiparametric data combination problems. A leading estimand in this class is the average treatment effect on the treated (ATT). Data combination problems are related to, but distinct from, the class of missing data problems with data missing at random (of which the average treatment effect (ATE) estimand is a special case). Our estimator also possesses a double robustness property. Our procedure may be used to efficiently estimate, among other objects, the ATT, the two-sample instrumental variables model (TSIV), counterfactual distributions, poverty maps, and semiparametric difference-in-differences. In an empirical application, we use our procedure to characterize residual Black–White wage inequality after flexibly controlling for “premarket” differences in measured cognitive achievement. Supplementary materials for this article are available online.