Australian & New Zealand Journal of Statistics最新文献

We suggest several constructions suitable to define the depth of set-valued observations with respect to a sample of convex sets or with respect to the distribution of a random closed convex set. With the concept of a depth, it is possible to determine if a given convex set should be regarded an outlier with respect to a sample of convex closed sets. Some of our constructions are motivated by the known concepts of half-space depth and band depth for function-valued data. A novel construction derives the depth from a family of non-linear expectations of random sets. Furthermore, we address the role of positions of sets for evaluation of their depth. Two case studies concern interval regression for Greek wine data and detection of outliers in a sample of particles.

For modelling the location of pyramidal cells in the human cerebral cortex, we suggest a hierarchical point process in that exhibits anisotropy in the form of cylinders extending along the z-axis. The model consists first of a generalised shot noise Cox process for the xy-coordinates, providing cylindrical clusters, and next of a Markov random field model for the z-coordinates conditioned on the xy-coordinates, providing either repulsion, aggregation or both within specified areas of interaction. Several cases of these hierarchical point processes are fitted to two pyramidal cell data sets, and of these a final model allowing for both repulsion and attraction between the points seem adequate. We discuss how the final model relates to the so-called minicolumn hypothesis in neuroscience.

In survey sampling studies, statistical inference can be constructed either using design based randomisation or super population model. Design-based inference using judgement post-stratified (JPS) sampling is available in the literature. This paper develops statistical inference based on super population model in a finite population setting using JPS sampling design. For a JPS sample, first a simple random sample (SRS) is constructed without replacement. The sample units in this SRS are then stratified based on judgement ranking in a small comparison set to induce a data structure in the sample. The paper shows that the mean of a JPS sample is model unbiased and has smaller mean square prediction error (MSPE) than the MSPE of a simple random sample mean. Using an unbiased estimator of the MSPE, the paper also constructs prediction confidence interval for the population mean. A small-scale empirical study shows that the JPS sample predictor performs better than an SRS predictor when the quality of ranking information in JPS sampling is not poor. The paper also shows that the coverage probabilities of prediction intervals are very close to the nominal coverage probability. Proposed inferential procedure is applied to a real data set obtained from an agricultural research farm.

It was a major breakthrough when design-based stereological methods for vertical sections were developed by Adrian Baddeley and coworkers in the 1980s. Most importantly, it was shown how to estimate in a design-based fashion surface area from observations in random vertical sections with uniform position and uniform rotation around the vertical axis. The great practical importance of these developments is due to the fact that some biostructures can only be recognised on vertical sections. Later, local design-based estimation of mean particle volume from vertical sections was developed. In the present paper, we review these important advances in stereology. Quite recently, vertical sections have gained renewed interest, since it has been shown that mean particle shape can be estimated from such sections. These new developments are also reviewed in the present paper.

Screening designs are important for finding the factors that have a major effect on industrial experiments. In regard to quantitative factors, certain experimenters prefer three-level rather than two-level factors because having three levels can provide some assessments for capturing curvature in the response. In a recent paper, Jones and Nachtsheim, Journal of Quality Technology43, 1–15, proposed a new class of designs called definitive screening designs. Definitive screening designs have more favourable properties than classical screening designs. In this paper, we study the projection properties of three-level screening designs. The comparison is based on several criteria such as D-efficiency, G-efficiency, A-efficiency and average of variance over a range of models that include main effects, interaction and quadratic terms. New designs are generated as projections of the full designs into a smaller factor dimensional space. The best projections and their properties are presented in a tabular form.

Count data arising in various fields of applications are often under-reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood-based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.

The present paper proposes the focussed information criterion (FIC) to tackle the model selection problems pertinent to generalised linear models (GLM) for time series. As a first step towards constructing the FIC, we formally discuss the local asymptotic theory of quasi-maximum likelihood estimation for time series GLM under potential model misspecification. The general FIC formula is derived subsequently that is useful for the simultaneous selection of the order of the autoregressive response as well as a subset of important covariates. We also develop the average FIC (AFIC) that is instrumental in selecting an overall good model for a range of covariates and time regions and establish the equivalence of the AFIC with the classical Akaike's information criterion (AIC). We demonstrate our theory with the analysis of rainfall patterns in Melbourne by means of the logistic and Gamma regression models.

Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool, which allows one to describe the relationships among the variables of interest. From the Bayesian perspective, there are two sources of randomness: one is related to the multivariate distribution and the quantities that may parametrise the model, and the other has to do with the underlying graph, G, equivalent to describing the conditional independence structure of the model under consideration. In this paper, we propose a prior on G based on two loss components. One considers the loss in information one would incur in selecting the wrong graph, while the second penalises for large number of edges, favouring sparsity. We illustrate the prior on simulated data and on real datasets, and compare the results with other priors on G used in the literature. Moreover, we present a default choice of the prior as well as discuss how it can be calibrated so as to reflect available prior information.