Australian & New Zealand Journal of Statistics最新文献

Where the response variable in a big dataset is consistent with the variable of interest for small area estimation, the big data by itself can provide the estimates for small areas. These estimates are often subject to the coverage and measurement error bias inherited from the big data. However, if a probability survey of the same variable of interest is available, the survey data can be used as a training dataset to develop an algorithm to impute for the data missed by the big data and adjust for measurement errors. In this paper, we outline a methodology for such imputations based on an k-nearest neighbours (kNN) algorithm calibrated to an asymptotically design-unbiased estimate of the national total, and illustrate the use of a training dataset to estimate the imputation bias and the “fixed-k asymptotic” bootstrap to estimate the variance of the small area hybrid estimator. We illustrate the methodology of this paper using a public-use dataset and use it to compare the accuracy and precision of our hybrid estimator with the Fay–Harriot (FH) estimator. Finally, we also examine numerically the accuracy and precision of the FH estimator when the auxiliary variables used in the linking models are subject to undercoverage errors.

Generalised linear mixed regression models are fundamental in statistics. Modelling random effects that are shared by individuals allows for correlation among those individuals. There are many methods and statistical packages available for analysing data using these models. Most require some form of numerical or analytic approximation because the likelihood function generally involves intractable integrals over the latents. The Bayesian approach avoids this issue by iteratively sampling the full conditional distributions for various blocks of parameters and latent random effects. Depending on the choice of the prior, some full conditionals are recognisable while others are not. In this paper we develop a novel normal approximation for the random effects full conditional, establish its asymptotic correctness and evaluate how well it performs. We make the case for hierarchical binomial and Poisson regression models with canonical link functions, for hierarchical gamma regression models with log link and for other cases. We also develop what we term a sufficient reduction (SR) approach to the Markov Chain Monte Carlo algorithm that allows for making inferences about all model parameters by replacing the full conditional for the latent variables with a considerably reduced dimensional function of the latents. We expect that this approximation could be quite useful in situations where there are a very large number of latent effects, which may be occurring in an increasingly ‘Big Data’ world. In the sequel, we compare our methods with INLA, which is a particularly popular method and which has been shown to be excellent in terms of speed and accuracy across a variety of settings. Our methods appear to be comparable to theirs in terms of accuracy, while INLA was faster, for the settings we considered. In addition, we note that our methods and those of others that involve Gibbs sampling trivially handle parameters that are functions of multiple parameters, while INLA approximations do not. Our primary illustration is for a three-level hierarchical binomial regression model for data on health outcomes for patients who are clustered within physicians who are clustered within particular hospitals or hospital systems.

Data related to the counting of elements of variable character are frequently encountered in time series studies. This paper brings forward a new class of $��k�$th-order dependence-driven random coefficient mixed thinning integer-valued autoregressive time series model (DDRCMTINAR($��k�$)) to deal with such data. Stationarity and ergodicity properties of the proposed model are derived in detail. The unknown parameters are estimated by conditional least squares, and modified quasi-likelihood and asymptotic normality of the obtained parameter estimators is established. The performances of the adopted estimate methods are checked via simulations, which present that modified quasi-likelihood estimators perform better than the conditional least squares considering the proportion of within-$��\Omega �$ estimates in certain regions of the parameter space. The validity and practical utility of the model are investigated by epileptic seizure data and COVID-19 data of suspected cases in China.

Under the $��p�$-order generalised random coefficient autoregressive (GRCA($��p�$)) model with random coefficients $��{�\Phi �}_{�t�}�,�$ we propose a conditional self-weighted $��M�$ estimator of $��E�{�\Phi �}_{�t�}�$. We investigate the asymptotic normality of this estimator with possibly heavy-tailed random variables. Furthermore, a Wald test statistic is constructed for the linear restriction on the parameters. In addition, the simulation experiments are carried out to assess the finite sample performance of theoretical results. Finally, a real data analysis about the increase (%) in the number of construction projects this year over the same period of last year is provided.

Robust estimation is primarily concerned with providing reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. In modern penalised generalised linear models (GLMs), however, there is limited research on robust estimation that can provide weights to determine the outlier status of the observations. This article proposes a unified framework based on a large family of loss functions, a composite of concave and convex functions (CC-family). Properties of the CC-family are investigated, and CC-estimation is innovatively conducted via the iteratively reweighted convex optimisation (IRCO), which is a generalisation of the iteratively reweighted least squares in robust linear regression. For robust GLM, the IRCO becomes the iteratively reweighted GLM. The unified framework contains penalised estimation and robust support vector machine (SVM) and is demonstrated with a variety of data applications.