Australian & New Zealand Journal of Statistics最新文献

We develop and describe online algorithms for performing online semiparametric regression analyses. Earlier work on this topic is by Luts, Broderick and Wand (2014), Journal of Computational and Graphical Statististics, 23, 589–615, where online mean-field variational Bayes (MFVB) was employed. In this article we instead develop sequential Monte Carlo approaches to circumvent well-known inaccuracies inherent in variational approaches. For Gaussian response semiparametric regression models, our new algorithms share the online MFVB property of only requiring updating and storage of sufficient statistics quantities of streaming data. In the non-Gaussian case, accurate online semiparametric regression requires the full data to be kept in storage. The new algorithms allow for new options concerning accuracy–speed trade-offs for online semiparametric regression.

This paper considers identifying and estimating high-dimensional longitudinal data models with latent subgroups and clustered covariates. We propose a regularised approach to recover group structures while simultaneously detecting clusters of significant covariates. The consistency and asymptotic normality are established for the estimator under mild conditions. Besides, we develop an effective algorithm based on local quadratic approximation to optimise the objective function. The finite-sample performance is illustrated through extensive simulations, and the proposed method is applied to study the shift in the economic structure of European countries before and after the debt crisis.

Extreme value theory has constructed asymptotic properties of the sample maximum. This article concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution—the generalised extreme value distribution; however, the model in non-limiting cases is misspecified to a certain extent. We propose a plug-in type of nonparametric estimator that does not need model specification. Asymptotic properties of the distribution estimator are derived. The simulation study numerically investigates the relative performance in finite-sample cases. This study assumes that the underlying distribution of the original sample belongs to one of the Hall class, the Weibull class or the bounded class, whose types of the limiting distributions are all different: the Fréchet, Gumbel or Weibull. It is proven that the convergence rate of the parametric fitting estimator depends on both the extreme value index and the second-order parameter, and gets slower as the extreme value index tends to zero. On the other hand, the rate of the nonparametric estimator is proven to be independent of the extreme value index under certain conditions. The numerical performances of the parametric fitting estimator and the nonparametric estimator are compared, which shows that the nonparametric estimator performs better, especially for the extreme value index close to zero. Finally, we report two real case studies: the Potomac River peak stream flow (cfs) data and the Danish Fire Insurance data.

We introduce a novel family of projected distributions on the circle and the sphere, called the circular and spherical projected Cauchy distributions, as promising alternatives for modelling circular and spherical data. The circular distribution encompasses the wrapped Cauchy distribution as a special case while featuring a more convenient parameterisation. We also propose a generalised wrapped Cauchy distribution that includes an extra parameter, enhancing the fit of the distribution. In the spherical context, we impose two conditions on the scatter matrix of the Cauchy distribution, resulting in an elliptically symmetric distribution. Our projected distributions exhibit attractive properties such as a closed-form normalising constant and straightforward random value generation. The distribution parameters can be estimated using maximum likelihood, and we assess their bias through numerical studies. Further, we compare our proposed distributions with existing models with real datasets, demonstrating equal or superior fitting both with and without covariates.

A critical aspect of experimental designs is to determine the effective and efficient lower bounds of the discrepancy criterion in uniform designs. These lower bounds serve as benchmarks for measuring the design uniformity and for constructing uniform designs. Nowadays, symmetric discrepancy and projection weighted symmetric discrepancy are two commonly used discrepancy criteria. In this paper, we investigate the general lower bounds of these two discrepancies for symmetric multi-level designs and present sharp lower bounds for three-level designs, thereby complementing the existing lower bound theory of discrepancies in uniform designs. Several design examples are used to validate the theoretical results presented. Furthermore, we conduct two popular practical computer experiments to evaluate the performance of uniform designs based on these two discrepancies.