A simulation comparison of estimators for a regression coefficient under differential non-response

We consider the estimation of a regression coefficient in a linear regression when observations are missing due to nonresponse. Response is assumed to be determined by a nonobservable variable which is linearly related to an observable variable. The values of the observable variable are assumed to be available for the whole sample but the variable is not includsd in the regression relationship of interest . Several alternative estimators have been proposed for this situation under various simplifying assumptions. A sampling theory approach provides three alternative estimatrs by considering the observatins as obtained from a sub-sample, selected on the basis of the fully observable variable , as formulated by Nathan and Holt (1980). Under an econometric approach, Heckman (1979) proposed a two-stage (probit and OLS) estimator which is consistent under specificconditions. A simulation comparison of the four estimators and the ordinary least squares estimator , under multivariate normality of all the variables involved, indicates that the econometric approach estimator is not robust to departures from the conditions underlying its derivation, while two of the other estimators exhibit a similar degree of stable performance over a wide range of conditions. Simulations for a non-normal distribution show that gains in performance can be obtained if observations on the independent variable are available for the whole population.     

Approximate tests of hypotheses in regression models with grouped data

Techniques for testing hypotheses about parameters in the regression models under the situation of grouped data are provided. A test statistic similar to conventional F statistic is considered. A simulation study performed for a few cases shows that the proposed statistic has an approximate F distribution and is useful in applications.     

A table of predictive success probabilities for logistic regression

A table of expected success rates under normally distributed success logit, used in conjunction with logistic regression analysis, enables easy calculation of expected win for betting on success of a future dichotomous trial.     

On a superiority problem in misspecified restricted linear models

Razzaghi (1987) conjectures that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency, This conjecture is proved to be correct.     

A distance based regression model for prediction with mixed data

A multiple regression method based on distance analysis and metric scaling is proposed and studied. This method allow us to predict a continuous response variable from several explanatory variables, is compatible with the general linear model and is found to be useful when the predictor variables are both continuous and categorical. Real data examples are given to illustrate the results obtained.     

Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs

ABSTRACT

This study develops methods for conducting uniform inference on quantile treatment effects for sharp regression discontinuity designs. We develop a score test for the treatment significance hypothesis and Wald-type tests for the hypotheses related to treatment significance, homogeneity, and unambiguity. The bias from the nonparametric estimation is studied in detail. In particular, we show that under some conditions, the asymptotic distribution of the score test is unaffected by the bias, without under-smoothing. For situations where the conditions can be restrictive, we incorporate a bias correction into the Wald tests and account for the estimation uncertainty. We also provide a procedure for constructing uniform confidence bands for quantile treatment effects. As an empirical application, we use the proposed methods to study the effect of cash-on-hand on unemployment duration. The results reveal pronounced treatment heterogeneity and also emphasize the importance of considering the long-term unemployed.     

Estimating common parameters of growth curve models under a quadratic loss

Consider the problem of estimating the common matrix of several growth curve models with possibly different unknown covariance matrices under the quadratic loss. The paper gives a combined estimator with a smaller risk than MLE of each growth curve model.     

Errors-in-variables regression using estimated latent variables

This note considers a method for estimating regression parameters from the data containing measurement errors using some natural estimates of the unobserved explanatory variables. It is shown that the resulting estimator is consistent not only in the usual linear regression model but also in the probit model and regression models with censoship or truncation. However, it fails to be consistent in nonlinear regression models except for special cases.     

Estimation and selection procedures in regression: An L1 approach

The authors consider the problem of estimating a regression function go involving several variables by the closest functional element of a prescribed class _G that is closest to it in the L₁ norm. They propose a new estimator ? based on independent observations and give explicit finite sample bounds for the L₁distance between ?g and go. They apply their estimation procedure to the problem of selecting the smoothing parameter in nonparametric regression.     

A global risk assessment model for civil wars

In this study, we construct a multivariate model that assesses the risk of an outbreak of civil war in a country over a period of 5 years into the future. In addition to structural factors of state weakness, which have dominated the literature on civil war onset, this model includes repression of basic human rights to personal integrity – an important harbinger of wars to come – as an aspect of state behavior. Our aim is not to explore the causal factors of civil war onset, but to build a model that includes indicators that correlate with civil war outbreak and may be used to predict it. Based on two versions of the model – logit and neural network – out-of-sample risk assessments for three different time periods are generated and compared to the historical record of civil war outbreak during those years. In addition, the model’s ability to produce in-sample risk assessments over a 5-year period is tested. Finally, we compute truly predictive civil war risk assessments for all countries for which data are available, for the years 2008–2012. The analyses show that with a relatively simple model and based on publicly available data sources, meaningful civil war risk assessments can be computed. The quality of the predictions exceeds that of prominent studies, in which the risk of interstate war is assessed.