A true simulation study of three estimators at equal protection of respondents in randomized response sampling

In this study, three different estimators for estimating the proportion of a sensitive attribute in survey sampling are compared at equal protection of the respondents. The three estimators considered are due to Odumade and Singh (2009, Comm. Statist. Theory Methods) , Singh and Sedory (2011, Sociological Methods and Research) and a new estimator obtained by minimizing a chi‐squared distance. A SAS Macro is developed to compare these three estimators using a simulation study at equal protection of the respondents. A set of data from a real face‐to‐face interview was collected using two decks of cards and has been analyzed. The results are discussed.     

Adjusting for Non‐Response in Population‐Based Case‐Control Studies

In this paper we discuss the analysis of data from population‐based case‐control studies when there is appreciable non‐response. We develop a class of estimating equations that are relatively easy to implement. For some important special cases, we also provide efficient semi‐parametric maximum‐likelihood methods. We compare the methods in a simulation study based on data from the Women's Cardiovascular Health Study discussed in Arbogast et al. (Estimating incidence rates from population‐based case‐control studies in the presence of non‐respondents, Biometrical Journal 44, 227–239, 2002).     

Estimation of a k-monotone density: characterizations, consistency and minimax lower bounds

The classes of monotone or convex (and necessarily monotone) densities on     can be viewed as special cases of the classes of k - monotone densities on     . These classes bridge the gap between the classes of monotone (1-monotone) and convex decreasing (2-monotone) densities for which asymptotic results are known, and the class of completely monotone (∞-monotone) densities on     . In this paper we consider non-parametric maximum likelihood and least squares estimators of a k -monotone density g ₀. We prove existence of the estimators and give characterizations. We also establish consistency properties, and show that the estimators are splines of degree k −1 with simple knots. We further provide asymptotic minimax risk lower bounds for estimating the derivatives     , at a fixed point x ₀ under the assumption that     .     

Small‐scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison

Empirical Bayes methods of estimating the local false discovery rate (LFDR) by maximum likelihood estimation (MLE), originally developed for large numbers of comparisons, are applied to a single comparison. Specifically, when assuming a lower bound on the mixing proportion of true null hypotheses, the LFDR MLE can yield reliable hypothesis tests and confidence intervals given as few as one comparison. Simulations indicate that constrained LFDR MLEs perform markedly better than conventional methods, both in testing and in confidence intervals, for high values of the mixing proportion, but not for low values. (A decision‐theoretic interpretation of the confidence distribution made those comparisons possible.) In conclusion, the constrained LFDR estimators and the resulting effect‐size interval estimates are not only effective multiple comparison procedures but also they might replace p‐values and confidence intervals more generally. The new methodology is illustrated with the analysis of proteomics data.     

Distribution of residual autocorrelations for multiplicative seasonal ARMA models with uncorrelated but nonindependent error terms

In this paper, we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving‐average models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption on the error terms in order to extend the range of applications of the seasonal autoregressive moving‐average models. We study the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations under weak assumptions on noise. We establish the asymptotic behavior of the proposed statistics. A set of Monte Carlo experiments and an application to monthly mean total sunspot number are presented.