Australian & New Zealand Journal of Statistics最新文献

In modern data analysis, it is common to use machine learning methods to predict outcomes on unlabelled datasets and then use these pseudo-outcomes in subsequent statistical inference. Inference in this setting is often called post-prediction inference. We propose a novel assumption-lean framework for statistical inference under post-prediction setting, called prediction de-correlated inference (PDC). Our approach is safe, in the sense that PDC can automatically adapt to any black-box machine-learning model and consistently outperform the supervised counterparts. The PDC framework also offers easy extensibility for accommodating multiple predictive models. Both numerical results and real-world data analysis demonstrate the superiority of PDC over the state-of-the-art methods.

Seasonal autoregressive (SAR) time series models have been extended to fit time series exhibiting multiple seasonalities. However, hardly any research in Bayesian literature has been done on modelling multiple seasonalities. In this article, we propose a full Bayesian analysis of triple SAR (TSAR) models for time series with triple seasonality, considering identification, estimation and prediction for these TSAR models. In this Bayesian analysis of TSAR models, we assume the model errors to be normally distributed and the model order to be a random variable with a known maximum value, and we employ the g prior for the model coefficients and variance. Accordingly, we first derive the posterior mass function of the TSAR order in closed form, which then enables us to identify the best order of TSAR model as the order value with the highest posterior probability. In addition, we derive the conditional posteriors to be a multivariate normal for the TSAR coefficients and to be an inverse gamma for the TSAR variance; also, we derive the conditional predictive distribution to be a multivariate normal for future observations. Since these derived conditional distributions are in closed forms, we introduce the Gibbs sampler to present the Bayesian analysis of TSAR models and to easily produce multiple-step-ahead predictions. Using Julia programming language, we conduct an extensive simulation study, aiming to evaluate the accuracy of our proposed full Bayesian analysis for TSAR models. In addition, we apply our work on time series to hourly electricity load in some European countries.

The cos-max method is a little-known method of identifying collinearities. It is based on the cos-max transformation, which makes minimal adjustment to a set of vectors to create orthogonal components with a one-to-one correspondence between the original vectors and the components. The aim of the transformation is that each vector should be close to the orthogonal component with which it is paired. Vectors involved in a collinearity must be adjusted substantially in order to create orthogonal components, while other vectors will typically be adjusted far less. The cos-max method uses the size of adjustments to identify collinearities. It gives a coherent relationship between collinear sets of variables and variance inflation factors (VIFs) and identifies collinear sets using more information than traditional methods. In this paper we describe these features of the method and examine its performance in examples, comparing it with alternative methods. In each example, the collinearities identified by the cos-max method only contained variables with high VIFs and contained all variables with high VIFs. The collinearities identified by other methods did not have such a close link to VIFs. Also, the collinearities identified by the cos-max method were as simple as or simpler than those given by other methods, with less overlap between collinearities in the variables that they contained.

Often, causal mediation analysis is of interest when both the mediator and the final outcome are repeatedly measured, but limited work has been done for this situation (as opposed to where only the mediator is repeatedly measured). Available methods are primarily based on parametric models and tend to be sensitive to model assumptions. This article presents semiparametric, continuous-time models to provide a flexible and robust approach to causal mediation analysis for longitudinal data, which allows these data to be unbalanced or irregular. Specifically, the method uses spline linear mixed-effects models for the mediator and for the final outcome, with a two-step approach to model-fitting in which a predicted mediator is used as a covariate in the final outcome model. The models allow flexible functions for both the mean and individual response functions for each outcome. We derive estimated natural direct and indirect effects as a function of time using an extended mediation formula and sequential ignorability assumption. In simulation studies, we compare properties of estimated direct and indirect effects, and a delta method estimate of the standard error of the latter, under alternative approaches for predicting the mediator. The approach is illustrated using harmonised data from two cohort studies to examine attention as a mediator of the effect of prenatal tobacco exposure on externalising behaviour in children.