Australian & New Zealand Journal of Statistics最新文献

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.