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

This article proposes multivariate copula models for hierarchical data. They account for two types of correlation: one is between variables measured on the same unit, and the other is a correlation between units in the same cluster. This model is used to carry out copula regression for hierarchical data that gives cluster-specific prediction curves. In the simple case where a cluster contains two units and where two variables are measured on each one, the new model is constructed with a $��D�$-vine. The proposed copula density is expressed in terms of three copula families. When the copula families and the marginal distributions are normal, the model is equivalent to a normal linear mixed model with random cluster-specific intercepts. Methods to select the three copula families and to estimate their parameters are proposed. We perform Monte Carlo studies of the sampling properties of these estimators and of out-of-sample predictions. The new model is applied to a dataset on the marks of students in several schools.

Epidemic trajectories can be substantially impacted by people modifying their behaviours in response to changes in their perceived risk of spreading or contracting the disease. However, most infectious disease models assume a stable population behaviour. We present a flexible new class of models, called behavioural change individual-level models (BC-ILMs), that incorporate both individual-level covariate information and a data-driven behavioural change effect. Focusing on spatial BC-ILMs, we consider four “alarm” functions to model the effect of behavioural change as a function of infection prevalence over time. Through simulation studies, we find that if behavioural change is present, using an alarm function, even if specified incorrectly, will result in an improvement in posterior predictive performance over a model that assumes stable population behaviour. The methods are applied to data from the 2001 U.K. foot and mouth disease epidemic. The results show some evidence of a behavioural change effect, although it may not meaningfully impact model fit compared to a simpler spatial ILM in this dataset.

The generalized extreme value (GEV) distribution is a popular model for analyzing and forecasting extreme weather data. To increase prediction accuracy, spatial information is often pooled via a latent Gaussian process (GP) on the GEV parameters. Inference for GEV-GP models is typically carried out using Markov Chain Monte Carlo (MCMC) methods, or using approximate inference methods such as the integrated nested Laplace approximation (INLA). However, MCMC becomes prohibitively slow as the number of spatial locations increases, whereas INLA is applicable in practice only to a limited subset of GEV-GP models. In this article, we revisit the original Laplace approximation for fitting spatial GEV models. In combination with a popular sparsity-inducing spatial covariance approximation technique, we show through simulations that our approach accurately estimates the Bayesian predictive distribution of extreme weather events, is scalable to several thousand spatial locations, and is several orders of magnitude faster than MCMC. A case study in forecasting extreme snowfall across Canada is presented.

We consider random sample splitting for estimation and inference in high-dimensional generalized linear models (GLMs), where we first apply the lasso to select a submodel using one subsample and then apply the debiased lasso to fit the selected model using the remaining subsample. We show that a sample splitting procedure based on the debiased lasso yields asymptotically normal estimates under mild conditions and that multiple splitting can address the loss of efficiency. Our simulation results indicate that using the debiased lasso instead of the standard maximum likelihood method in the estimation stage can vastly reduce the bias and variance of the resulting estimates. Furthermore, our multiple splitting debiased lasso method has better numerical performance than some existing methods for high-dimensional GLMs proposed in the recent literature. We illustrate the proposed multiple splitting method with an analysis of the smoking data of the Mid-South Tobacco Case–Control Study.

In many biomedical applications, there is a need to build risk-adjustment models based on clustered data. However, methods for variable selection that are applicable to clustered discrete data settings with a large number of candidate variables and potentially large cluster sizes are lacking. We develop a new variable selection approach that combines within-cluster resampling techniques with penalized likelihood methods to select variables for high-dimensional clustered data. We derive an upper bound on the expected number of falsely selected variables, demonstrate the oracle properties of the proposed method and evaluate the finite sample performance of the method through extensive simulations. We illustrate the proposed approach using a colon surgical site infection data set consisting of 39,468 individuals from 149 hospitals to build risk-adjustment models that account for both the main effects of various risk factors and their two-way interactions.

In this article, we develop an innovative, robust method for jointly analyzing longitudinal count and binary responses. The method is useful for bounding the influence of potential outliers in the data when estimating the model parameters. We use a log-linear model for the count response and a logistic regression model for the binary response, where the two response processes are linked through a set of association parameters. The asymptotic properties of the robust estimators are briefly studied. The empirical properties of the estimators are studied based on simulations. The study shows that the proposed estimators are approximately unbiased and also efficient when fitting a joint model to data contaminated with outliers. We also apply the proposed method to some real longitudinal survey data obtained from a health study.

This article focuses on detecting change points in high-dimensional linear regression models with piecewise constant regression coefficients, moving beyond the conventional reliance on strict Gaussian or sub-Gaussian noise assumptions. In the face of real-world complexities, where noise often deviates into uncertain or heavy-tailed distributions, we propose two tailored algorithms: a dynamic programming algorithm (DPA) for improved localization accuracy, and a binary segmentation algorithm (BSA) optimized for computational efficiency. These solutions are designed to be flexible, catering to increasing sample sizes and data dimensions, and offer a robust estimation of change points without requiring specific moments of the noise distribution. The efficacy of DPA and BSA is thoroughly evaluated through extensive simulation studies and application to real datasets, showing their competitive edge in adaptability and performance.

Missing data reduce the representativeness of the sample and can lead to inference problems. In this article, we apply the Bayesian jackknife empirical likelihood (BJEL) method for inference on data that are missing at random, as well as for causal inference. The semiparametric fractional imputation estimator, propensity score-weighted estimator, and doubly robust estimator are used for constructing the jackknife pseudo values, which are needed for conducting BJEL-based inference with missing data. Existing methods, such as normal approximation and JEL, are compared with the BJEL approach in a simulation study. The proposed approach shows better performance in many scenarios in terms of credible intervals. Furthermore, we demonstrate the application of the proposed approach for causal inference problems in a study of risk factors for impaired kidney function.

Nonparametric estimation of a regression curve becomes crucial when the underlying dependence structure between covariates and responses is not explicit. While existing literature has addressed single change-point estimation for regression curves, the problem of multiple change points remains unresolved. In an effort to bridge this gap, this article introduces a nonparametric estimator for multiple change points by minimizing a penalized weighted sum of squared residuals, presenting consistent results under mild conditions. Additionally, we propose a cross-validation-based procedure that possesses the advantage of being tuning-free. Our simulation results showcase the competitive performance of these new procedures when compared with state-of-the-art methods. As an illustration of their utility, we apply these procedures to a real dataset.

The additive hazards model is one of the most commonly used models for regression analysis of failure time data, and many methods have been developed for its estimation. In this article, we consider the situation where one observes informatively interval-censored data arising from case-cohort studies where covariate information is collected only for a small subcohort of study subjects. By informative or dependent censoring, we mean that the failure time of interest and the censoring mechanism may be correlated. For estimation, we will develop a sieve inverse probability weighting estimation procedure with the use of Bernstein polynomials. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed method works well in practical situations. An example is also provided.