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Summary. Primary analysis of case–control studies focuses on the relationship between disease D and a set of covariates of interest (Y, X). A secondary application of the case–control study, which is often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated owing to the case–control sampling,...
Summary. The conventional Wilcoxon or Mann–Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pretreatment variables. We propose an approach to adjust the Mann–Whitney test by correcting the potential bias via consistently...
Summary. Group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect, a lack of an effect or concerns about patient safety. In many studies, the response of clinical interest is measured some time after the start of treatment and there are subjects at each interim analysis who have been treated but are yet to respond...
Summary. Stability selection was recently introduced by Meinshausen and Bühlmann as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection procedure to subsamples of the data. We introduce a variant, called complementary pairs stability selection, and derive bounds both on the expected number of...
Summary. Subsampling and block‐based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as the subsampling window width and block size in the block‐based bootstrap. In empirical work, using different bandwidth parameters could lead to different inference results, but traditional...
Summary. The paper is concerned with inference based on the mean function of a functional time series. We develop a normal approximation for the functional sample mean and then focus on the estimation of the asymptotic variance kernel. Using these results, we develop and asymptotically justify testing procedures for the equality of means in two functional samples exhibiting temporal dependence. Evaluated...
Summary. Non‐Gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model offers a very popular and flexible approach...
Summary. The paper develops a new estimation of non‐parametric regression functions for clustered or longitudinal data. We propose to use Cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously. We further prove that the estimator proposed is as asymptotically efficient as if the covariance matrix were known. A Monte...
Summary. In conditionally heteroscedastic models, the optimal prediction of powers, or logarithms, of the absolute value has a simple expression in terms of the volatility and an expectation involving the independent process. A natural procedure for estimating this prediction is to estimate the volatility in the first step, for instance by Gaussian quasi‐maximum‐likelihood or by least absolute deviations,...
Summary. Experimenters often use post‐stratification to adjust estimates. Post‐stratification is akin to blocking, except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment. We analyse both post‐stratification and blocking under the Neyman–Rubin model and compare the efficiency of these designs. We derive the variances for...
Summary. The inspection of residuals is a fundamental step for investigating the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed as an empirical counterpart of the Campbell equilibrium equation for marked Gibbs point processes. The paper focuses on stationary marked Gibbs point processes and deals with asymptotic...
The paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors. Theoretically, we obtain asymptotic normality for the M‐estimator of the regression parameter under mild conditions and establish a uniform Bahadur representation for recursive M‐estimators. Methodologically, we extend the recently proposed self‐normalized approach of Shao...
Summary. We study the heteroscedastic partially linear single‐index model with an unspecified error variance function, which allows for high dimensional covariates in both the linear and the single‐index components of the mean function. We propose a class of consistent estimators of the parameters by using a proper weighting strategy. An interesting finding is that the linearity condition which is...
Summary. The paper develops non‐parametric methods based on contact intervals for the analysis of infectious disease data. The contact interval from person i to person j is the time between the onset of infectiousness in i and infectious contact from i to j, where we define infectious contact as a contact sufficient to infect a susceptible individual. The hazard function of the contact interval distribution...
Summary. In data sets with many more features than observations, independent screening based on all univariate regression models leads to a computationally convenient variable selection method. Recent efforts have shown that, in the case of generalized linear models, independent screening may suffice to capture all relevant features with high probability, even in ultrahigh dimension. It is unclear...
A methodology for the simultaneous Bayesian non‐parametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in detail. Efficient slice sampling methods are...
Estimation of high dimensional covariance matrices is known to be a difficult problem, has many applications and is of current interest to the larger statistics community. In many applications including the so‐called ‘large p, small n’ setting, the estimate of the covariance matrix is required to be not only invertible but also well conditioned. Although many regularization schemes attempt to do this,...
Summary. Sparsity is an essential feature of many contemporary data problems. Remote sensing, various forms of automated screening and other high throughput measurement devices collect a large amount of information, typically about few independent statistical subjects or units. In certain cases it is reasonable to assume that the underlying process generating the data is itself sparse, in the sense...
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