Canadian Journal of Statistics-Revue Canadienne De Statistique最新文献

Two senior statisticians/data scientists reflect on the challenges arising from the analysis of increasingly complex data using robustness. They include some thoughts on the types of robust analysis that will be needed in the future, while cognizant of our very limited ability to successfully predict the future.

This article describes the founding and growth of the Canadian Statistical Sciences Institute (CANSSI), starting from its early roots and continuing through to establishment as a mature research enterprise. The goal is to present a historical record of events and activities that were important in the development of CANSSI.

In this article, we first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with nonprobability survey samples. We highlight the important research contributions to the field of survey sampling in general and the two topics in particular by Canadian survey statisticians. We then propose new inferential procedures for analyzing nonprobability survey samples through the pseudo empirical likelihood approach. The proposed methods lead to point estimators asymptotically equivalent to those discussed in the recent literature but with more desirable features on confidence intervals such as range-respecting and data-driven orientation. Results from a simulation study demonstrate the superiority of the proposed methods in dealing with binary response variables.

Bayesian inference and Markov chain Monte Carlo methods are vigorous areas of statistical research. Here we reflect on some recent developments and future directions in these fields.

With the development of science and technology, massive datasets stored in multiple machines are increasingly prevalent. It is known that traditional statistical methods may be infeasible for analyzing large datasets owing to excessive computing time, memory limitations, communication costs, and privacy concerns. This article develops divide-and-conquer empirical likelihood (DEL) and divide-and-conquer exponentially tilted empirical likelihood (DETEL) methods for the distributed computing setting. We investigate the theoretical properties of the DEL and DETEL estimators. In particular, we derive upper bounds for the mean squared errors of the DEL and DETEL estimators, and, under some mild conditions, we prove the consistency and the asymptotic normality of the proposed estimators. Simulation studies and a real data analysis are carried out to demonstrate the finite-sample performance of the proposed methods.

Exposures are often misclassified in observational studies. Any analysis that does not make proper adjustments for misclassification may result in biased estimates of model parameters, resulting in distorted inference. Settings where a multicategory exposure variable has more than two nominal categories or where no validation data are available to assess misclassification probabilities are common in practice but seldom considered in the literature. This article presents a novel method of analyzing cohort data with a misclassified, multicategory exposure variable and a binary response variable that uses instrumental variables in lieu of a validation dataset. First, a sufficient condition is obtained for model identifiability. Then, methods for model estimation and inference are proposed after adopting a sufficient condition for identifiability. We consider a variational Bayesian inference procedure aided by automatic differentiation along with Markov chain Monte Carlo-based computation. Operating characteristics of the proposed methods are assessed through simulation studies. For the purpose of illustration, the proposed Bayesian methods are applied to the U.S. breast cancer mortality data sampled from the Surveillance Epidemiology and End Results database, where reported treatment therapy is the misclassified multicategory exposure variable.

We identify sufficient conditions to resolve the identification problem under nonignorable missingness, especially the identifiability of the observed likelihood when some of the covariate values are missing not at random, or, simultaneously, the response is also missing not at random. It is more difficult to tackle these cases than the nonignorable nonresponse case, and, to the best of our knowledge, the simultaneously missing case has never been discussed before. Under these conditions, we propose some parameter estimation methods. As an illustration, when some of the covariate values are missing not at random, we adopt a semiparametric logistic model with a tilting parameter to model the missingness mechanism and use an imputed estimating equation based on the generalized method of moments to estimate the parameters of interest and the tilting parameter simultaneously. This approach avoids the requirement for other independent surveys or a validation sample to estimate the unknown tilting parameter. The asymptotic properties of our proposed estimators are derived, and the proofs can be modified to show that our methods of estimation, which are based on inverse probability weighting, augmented inverse probability weighting, and estimating equation projection, have the same asymptotic efficiency when the tilting parameter is either known or unknown but estimated by some other method. In simulation studies, we compare our methods with various alternative approaches and find that our methods are more robust and effective.

Precision medicine describes health care where patient-level data are used to inform treatment decisions. Within this framework, dynamic treatment regimes (DTRs) are sequences of decision rules that take individual patient information as input data and then output treatment recommendations. DTR estimation from observational data typically relies on the assumption of no interference: i.e., the outcome of one individual is unaffected by the treatment assignment of others. However, in many social network contexts, such as friendship or family networks, and for many health concerns, such as infectious diseases, this assumption is questionable. We investigate the DTR estimation method of dynamic weighted ordinary least squares (dWOLS), which boasts of easy implementation and the so-called double-robustness property, but relies on the assumption of no interference. We define a network propensity function and build on it to establish an implementation of dWOLS that remains doubly robust under interference associated with network links. The method's properties are demonstrated via simulation and applied to data from the Population Assessment of Tobacco and Health (PATH) study to investigate cigarette dependence within two-person household networks.

This article develops a two-step procedure for estimating the unknown parameters in a model that contains a fixed but large number of covariates, more moment conditions than unknown parameters, and responses that are missing at random. We propose a sufficient dimension reduction method to be implemented in the first step and prove that the method is asymptotically valid. In the second step, we apply three well-known missing data handling mechanisms together with the generalized method of moments to the reduced-dimensional subspace to obtain estimates of unknown parameters. We investigate the theoretical properties of the proposed methods, including the effects of dimension reduction on the asymptotic distributions of the estimators. Our results refute a claim in an earlier study that dimension reduction yields the same asymptotic distributions of estimators as when the reduced-dimensional structure is the true structure. We illustrate our method by way of a simulation study and a real clinical trial data example.

Quantiles are a fundamental concept in extreme value theory. They can be obtained from a minimization framework using an asymmetric absolute error loss criterion. The companion notion of expectiles, based on asymmetric squared rather than asymmetric absolute error loss minimization, has received substantial attention from the fields of actuarial science, finance, and econometrics over the last decade. Quantiles and expectiles can be embedded in a common framework of $��{�L�}^{�p�}�$-quantiles, whose extreme value properties have been explored very recently. Although this generalized notion of quantiles has shown potential for the estimation of extreme quantiles and expectiles, available estimators remain quite difficult to use: they suffer from substantial bias, and the question of the choice of the tuning parameter $��p�$ remains open. In this article, we work in a context of heavy tails and construct composite bias-reduced estimators of extreme quantiles and expectiles based on $��{�L�}^{�p�}�$-quantiles. We provide a discussion of the data-driven choice of $��p�$ and of the anchor $��{�L�}^{�p�}�$-quantile level in practice. The proposed methodology is compared with existing approaches on simulated data and real data.