Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Still-births among the offspring of male radiation workers at the Sellafield nuclear reprocessing plant: detailed results and statistical aspects

Summary. This study investigates whether there was evidence of increasing risk of still-birth with increasing paternal exposure to ionizing radiation received during employment at the Sellafield nuclear installation before the child was conceived. A significant positive association is found between the total paternal preconceptional exposure to external ionizing radiation and the risk of still-birth (after adjustment for year of birth, social class, birth order and paternal age, odds ratio at 100 mSv 1.24 (95% confidence interval 1.04–1.45)). A summary of the principal scientific findings of this study has been published in the Lancet . This paper describes in detail the statistical methods that were used in the investigation and presents the results in full.     

Living Arrangements, Employment Status, and the Economic Well-Being of Mothers: Evidence from Brazil, Chile, and the U.S

Using data from Brazil, Chile, and the U.S., we estimate country specific models of household income that characterize mothers according to their marital status, living arrangement, and employment status. We assess the predicted economic well-being of each type of mother relative to a benchmark of married mothers in the same country, and at various points in the income distribution. We find dramatic cross-country differences in the distribution of mothers across categories, but few differences in each type's relative economic status. In all three countries and at all points in the income distribution, mothers who are the only adults in their households have the lowest levels of predicted income, while married mothers—followed closely by cohabitors—have the highest levels.     

On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

Adaptive tests of regression functions via multiscale generalized likelihood ratios

Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. She derives the asymptotic joint distribution of the component tests and that of the proposed test under the null hypothesis. She also develops a simple method of selecting the smoothing parameters for the proposed test and presents two approximate methods for obtaining its P‐value. Finally, she evaluates the proposed test through simulations and illustrates its application to a set of real data.     

BURR CRITICAL VALUE APPROXIMATIONS FOR TESTS OF AUTOCORRELATION AND HETEROSCEDASTICITY

The paper evaluates the accuracy of Burr approximations of critical values and p-values for test a of autocorrelation and heteroscedasticity in the linear regression model.     

A modified random-effect procedure for combining risk difference in sets of 2×2 tables from clinical trials

Summary Meta-analyses of sets of clinical trials often combine risk differences from several 2×2 tables according to a random-effects model. The DerSimonian-Laird random-effects procedure, widely used for estimating the populaton mean risk difference, weights the risk difference from each primary study inversely proportional to an estimate of its variance (the sum of the between-study variance and the conditional within-study variance). Because those weights are not independent of the risk differences, however, the procedure sometimes exhibits bias and unnatural behavior. The present paper proposes a modified weighting scheme that uses the unconditional within-study variance to avoid this source of bias. The modified procedure has variance closer to that available from weighting by ideal weights when such weights are known. We studied the modified procedure in extensive simulation experiments using situations whose parameters resemble those of actual studies in medical research. For comparison we also included two unbiased procedures, the unweighted mean and a sample-size-weighted mean; their relative variability depends on the extent of heterogeneity among the primary studies. An example illustrates the application of the procedures to actual data and the differences among the results. This research was supported by Grant HS 05936 from the Agency for Health Care Policy and Research to Harvard University.     

Creating a reference to a complex emergency situation using time series methods: war in Guinea-Bissau 1998-1999

Impacts of complex emergencies or relief interventions have often been evaluated by absolute mortality compared to international standardized mortality rates. A better evaluation would be to compare with local baseline mortality of the affected populations. A projection of population-based survival data into time of emergency or intervention based on information from before the emergency may create a local baseline reference. We find a log-transformed Gaussian time series model where standard errors of the estimated rates are included in the variance to have the best forecasting capacity. However, if time-at-risk during the forecasted period is known then forecasting might be done using a Poisson time series model with overdispersion. Whatever, the standard error of the estimated rates must be included in the variance of the model either in an additive form in a Gaussian model or in a multiplicative form by overdispersion in a Poisson model. Data on which the forecasting is based must be modelled carefully concerning not only calendar-time trends but also periods with excessive frequency of events (epidemics) and seasonal variations to eliminate residual autocorrelation and to make a proper reference for comparison, reflecting changes over time during the emergency. Hence, when modelled properly it is possible to predict a reference to an emergency-affected population based on local conditions. We predicted childhood mortality during the war in Guinea-Bissau 1998-1999. We found an increased mortality in the first half-year of the war and a mortality corresponding to the expected one in the last half-year of the war.     

BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

Marginal and association regression models for longitudinal binary data with drop‐outs: A likelihood‐based approach

Longitudinal data often contain missing observations, and it is in general difficult to justify particular missing data mechanisms, whether random or not, that may be hard to distinguish. The authors describe a likelihood‐based approach to estimating both the mean response and association parameters for longitudinal binary data with drop‐outs. They specify marginal and dependence structures as regression models which link the responses to the covariates. They illustrate their approach using a data set from the Waterloo Smoking Prevention Project They also report the results of simulation studies carried out to assess the performance of their technique under various circumstances.