An Improvement of Poisson Approximation for Sums of Dependent Bernoulli Random Variables

This article uses the Stein-Chen method to obtain new non uniform bounds on the error of the cumulative distribution function of sums of dependent Bernoulli random variables and the Poisson cumulative distribution function. The bounds obtained in the present study are sharper than those reported in Teerapabolarn and Neammanee (2006 Teerapabolarn, K., Neammanee, K. (2006). Poisson approximation for sums of dependent Bernoulli random variables. Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis. 22:87–99. [Google Scholar]). Examples are provided to illustrate applications of the obtained results.     

The use of conditional cutoffs in a forward selection procedure

Using a forward selection procedure for selecting the best subset of regression variables involves the calculation of critical values (cutoffs) for an F-ratio at each step of a multistep search process. On dropping the restrictive (unrealistic) assumptions used in previous works, the null distribution of the F-ratio depends on unknown regression parameters for the variables already included in the subset. For the case of known σ, by conditioning the F-ratio on the set of regressors included so far and also on the observed (estimated) values of their regression coefficients, we obtain a forward selection procedure whose stepwise type I error does not depend on the unknown (nuisance) parameters. A numerical example with an orthogonal design matrix illustrates the difference between conditional cutoffs, cutoffs for the centralF-distribution, and cutoffs suggested by Pope and Webster.     

Formative Indicators and Effects of a Causal Model for Household Human Capital with Application

Dagum and Slottje (2000 Dagum , C. , Slottje , D. J. ( 2000 ). A new method to estimate the level and distribution of the household human capital with applications . Journal of Structural Change and Economic Dynamics 11 : 67 – 94 .[Crossref] , [Google Scholar]) estimated household human capital (HC) as a latent variable (LV) and proposed its monetary estimation by means of an actuarial approach. This paper introduces an improved method for the estimation of household HC as an LV by means of formative and reflective indicators in agreement with the accepted economic definition of HC. The monetary value of HC is used in a recursive causal model to obtain short- and long-term multipliers that measure the direct and total effects of the variables that determine household HC. The new method is applied to estimate US household HC for year 2004.     

Robustness of Bootstrap in Instrumental Variable Regression

This paper studies robustness of bootstrap inference methods for instrumental variable (IV) regression models. We consider test statistics for parameter hypotheses based on the IV estimator and generalized method of trimmed moments (GMTM) estimator introduced by ?í?ek (2008 ?í?ek's , P. ( 2008 ). General trimmed estimation: Robust approach to nonlinear and limited dependent variable models . Econometric Theory 24 : 1500 – 1529 .[Crossref], [Web of Science ®] , [Google Scholar], 2009 ?í?ek's , P. ( 2009 ). Generalized method of trimmed moments. Working paper, Tilburg University, Tilburg, Netherlands . [Google Scholar]), and compare the pairs and implied probability bootstrap approximations for these statistics by applying the finite sample breakdown point theory. In particular, we study limiting behaviors of the bootstrap quantiles when the values of outliers diverge to infinity but the sample size is held fixed. The outliers are defined as anomalous observations that can arbitrarily change the value of the statistic of interest. We analyze both just- and overidentified cases and discuss implications of the breakdown point analysis to the size and power properties of bootstrap tests. We conclude that the implied probability bootstrap test using the statistic based on the GMTM estimator shows desirable robustness properties. Simulation studies endorse this conclusion. An empirical example based on Romer's (1993 Romer , D. ( 1993 ). Openness and inflation: Theory and evidence . The Quarterly Journal of Economics 108 : 869 – 903 .[Crossref], [Web of Science ®] , [Google Scholar]) study on the effect of openness of countries to inflation rates is presented. Several extensions including the analysis for the residual bootstrap are provided.     

A hybrid approach to achieving both marginal and conditional balances for stratification variables in sequential clinical trials

Various methods exist in the literature for achieving marginal balance for baseline stratification variables in sequential clinical trials. One major limitation with balancing on the margins of the stratification variables is that there is an efficiency loss when the primary analysis is stratified. To preserve the efficiency of a stratified analysis one recently proposed approach balances on the crossing of the stratification variables included in the analysis, which achieves conditional balance for the variables. A hybrid approach to achieving both marginal and conditional balances in sequential clinical trials is proposed, which is applicable to both continuous and categorical stratification variables. Numerical results based on extensive simulation studies and a real dataset show that the proposed approach outperforms the existing ones and is particularly useful when both additive and stratified models are planned for a trial. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponentially weighted moving average control schemes with variable sampling intervals

The idea of using non-constant sampling intervals has been of interest in quality control applications since it was first suggested for the “skip-lot sampling plan” of Dodge. Recent interest has focused on the use of variable sampling interval (VSI) control schemes. VSI control schemes use a short sampling interval is given     

Modeling Association Between Two or More Categorical Variables that Allow for Multiple Category Choices

Multiple-response (or pick any/c) categorical variables summarize responses to survey questions that ask “pick any” from a set of item responses. Extensions to loglinear model methodology are proposed to model associations between these variables across all their items simultaneously. Because individual item responses to a multiple-response categorical variable are likely to be correlated, the usual chi-square distributional approximations for model-comparison statistics are not appropriate. Adjusted statistics and a new bootstrap procedure are developed to facilitate distributional approximations. Odds ratio and standardized Pearson residual measures are also developed to estimate specific associations and examine deviations from a specified model.     

A Stepwise AIC Method for Variable Selection in Linear Regression

In this article, we study stepwise AIC method for variable selection comparing with other stepwise method for variable selection, such as, Partial F, Partial Correlation, and Semi-Partial Correlation in linear regression modeling. Then we show mathematically that the stepwise AIC method and other stepwise methods lead to the same method as Partial F. Hence, there are more reasons to use the stepwise AIC method than the other stepwise methods for variable selection, since the stepwise AIC method is a model selection method that can be easily managed and can be widely extended to more generalized models and applied to non normally distributed data. We also treat problems that always appear in applications, that are validation of selected variables and problem of collinearity.     

Estimation of Population Mean Using Known Coefficient of Variation of the Study Character in the Presence of Non Response

Using the known coefficient of variation of the study character, generalized and regression-type estimators for the population mean using two phase sampling in the presence of non response were proposed and their properties have been studied. The conditions under which the proposed estimators are more efficient than the relevant estimators have been obtained. The empirical studies were given in the support of the problems in the case of positive and negative correlation between the study and the auxiliary characters which show the increase in the efficiency of the proposed estimators using known coefficient of variation of the study character with respect to the relevant estimators.     

On Variance-Stabilizing Multivariate Non Parametric Regression Estimation

The mean squared error (MSE)-minimizing local variable bandwidth for the univariate local linear estimator (the LL) is well-known. This bandwidth does not stabilize variance over the domain. Moreover, in regions where a regression function has zero curvature, the LL estimator is discontinuous. In this paper, we propose a variance-stabilizing (VS) local variable diagonal bandwidth matrix for the multivariate LL estimator. Theoretically, the VS bandwidth can outperform the multivariate extension of the MSE-minimizing local variable scalar bandwidth in terms of asymptotic mean integrated squared error and can avoid discontinuity created by the MSE-minimizing bandwidth. We present an algorithm for estimating the VS bandwidth and simulation studies.