International Statistical Review最新文献

The generalised regression estimator (GREG) uses auxiliary data that are available from the finite population to improve the efficiency of the estimator of a total (mean). Estimators of the variance of GREG that have been proposed in the sampling literature include those based on Taylor linearisation and the jackknife techniques. Approximations based on Taylor expansions are reasonable for large samples. However, when the sample size is small, the Taylor-based variance estimator has a large negative bias. The jackknife variance estimators overestimate the variance of GREG for small sample sizes. We offset these setbacks using a bootstrap procedure for estimating the variance of the GREG. The method uses a bootstrap population constructed with the model underlying the GREG estimator. Repeated samples are selected in the bootstrap population according to the design used to select the initial sample, and the variability associated with these bootstrap samples is used to compute the proposed bootstrap variance estimator. Simulations show that the new bootstrap estimator has a small bias for samples that have few observations.

Longitudinal studies play a prominent role in research on growth, change and/or decline in individuals, and in characterising the environmental and social factors which influence change. The essential feature of a longitudinal study is taking repeated measures of an outcome on the same set of individuals at multiple timepoints, thereby allowing investigators to characterise within subject changes during the measurement period. This paper provides an overview of how the basic design features and analysis of longitudinal studies are related to other study designs, including longitudinal clinical trials as well as repeated measures studies. I summarise the use of the linear mixed model as described in Laird and Ware for the analysis of a broad class of designs and present some applications in health and medicine.

Nan Laird has an enormous and growing impact on computational statistics. Her paper with Dempster and Rubin on the expectation-maximisation (EM) algorithm is the second most cited paper in statistics. Her papers and book on longitudinal modelling are nearly as impressive. In this brief survey, we revisit the derivation of some of her most useful algorithms from the perspective of the minorisation-maximisation (MM) principle. The MM principle generalises the EM principle and frees it from the shackles of missing data and conditional expectations. Instead, the focus shifts to the construction of surrogate functions via standard mathematical inequalities. The MM principle can deliver a classical EM algorithm with less fuss or an entirely new algorithm with a faster rate of convergence. In any case, the MM principle enriches our understanding of the EM principle and suggests new algorithms of considerable potential in high-dimensional settings where standard algorithms such as Newton's method and Fisher scoring falter.

We provide a critical review on calibration methods developed in three different areas: survey sampling, missing data analysis and causal inference. We highlight the connections and variations of calibration techniques used in missing data analysis and causal inference to conventional calibration weighting and estimation in survey sampling and provide a common framework through model-calibration and empirical likelihood to unify different calibration methods proposed in recent literature. The goal is to demonstrate the success and effectiveness of calibration methods in achieving some highly desired properties for missing data analysis and causal inference.