Australian & New Zealand Journal of Statistics最新文献

In this paper, using the notion of data depth, we describe two classes of affine invariant test statistics for the one-sample location problem. The tests are implemented through the idea of permutation tests. The performance of the test against some competitors is investigated with an extensive simulation study. It is observed that the tests perform well when compared to their competitors for a wide spectrum of alternatives. If the proposed test is defined based on a moment-free depth function, then it is not inherently required to have finite moments of any order and the tests have broader applicability than some of the existing tests. The robustness property of the proposed tests is considered with a simulation study. Finally, we apply the tests to a real data example.

The Higher School Certificate (HSC) is the credential awarded to secondary school students in New South Wales (NSW), Australia. This paper reviews the current moderation process of the HSC and introduces and compares a range of modern statistical methods. With a comprehensive analysis of the complete 2013–2016 HSC results, we show that the monotone spline regression with the Huber loss function consistently beats the existing moderation method. With its simple structure, fast execution and improved effectiveness, this new moderation model is an ideal replacement of the in-force quadratic for the HSC practice in NSW.

We forecast the old-age dependency ratio for Australia under various pension age proposals, and estimate a pension age scheme that will provide a stable old-age dependency ratio at a specified level. Our approach involves a stochastic population forecasting method based on coherent functional data models for mortality, fertility and net migration, which we use to simulate the future age-structure of the population. Our results suggest that the Australian pension age should be increased to 68 by 2030, 69 by 2036 and 70 by 2050, in order to maintain the old-age dependency ratio at 23%, just above the 2018 level. Our general approach can easily be extended to other target levels of the old-age dependency ratio and to other countries.

Adversarial risk analysis (ARA) is an upcoming methodology that is considered to have advantages over the traditional decision-theoretic and game-theoretic approaches. ARA solutions for first-price sealed-bid (FPSB) auctions have been found but only under strong assumptions which make the model somewhat unrealistic. In this paper, we use ARA methodology to model FPSB auctions using more realistic assumptions. We define a new utility function that considers bidders’ wealth, we assume a reserve price and find solutions not only for risk-neutral but also for risk-averse as well as risk-seeking bidders. We model the problem using ARA for non-strategic play and level-k thinking solution concepts.

Various non-parametric goodness of fit tests have already been investigated in the literature. However, those tests are rarely used in the case of missing observations. We here study the goodness of fit test for missing data based on L_p distances along with Kolmogorov–Smirnov and Cramer–von-Mises distances when missingness occurs at random. The asymptotic distributions of the proposed test statistics have been derived under contiguous alternatives that enable us to investigate the asymptotic local power of the tests. We also study the performance of the tests for finite samples using simulation, and the tests perform well for those cases. The usefulness of the tests is illustrated on three real data sets.

In this paper, we analysed classification rules under Bayesian decision theory. The setup we considered here is fairly general, which can represent all possible parametric models. The Bayes classification rule we investigated minimises the Bayes risk under general loss functions. Among the existing literatures, the 0-1 loss function appears most frequently, under which the Bayes classification rule is determined by the posterior predictive densities. Theoretically, we extended the Bernstein–von Mises theorem to the multiple-sample case. On this basis, the oracle property of Bayes classification rule has been discussed in detail, which refers to the convergence of the Bayes classification rule to the one built from the true distributions, as the sample size tends to infinity. Simulations show that the Bayes classification rules do have some advantages over the traditional classifiers, especially when the number of features approaches the sample size.

We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.

In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas are continually being annexed into Data Science. For example, biometrics was traditionally statistics for agriculture in all its forms but now, in Data Science, it means the study of characteristics that can be used to identify an individual. Examples of non-intrusive measurements include height, weight, fingerprints, retina scan, voice, photograph/video (facial landmarks and facial expressions) and gait. A multivariate analysis of such data would be a complex project for a statistician, but a software engineer might appear to have no trouble with it at all. In any applied-statistics project, the statistician worries about uncertainty and quantifies it by modelling data as realisations generated from a probability space. Another approach to uncertainty quantification is to find similar data sets, and then use the variability of results between these data sets to capture the uncertainty. Both approaches allow ‘error bars’ to be put on estimates obtained from the original data set, although the interpretations are different. A third approach, that concentrates on giving a single answer and gives up on uncertainty quantification, could be considered as Data Engineering, although it has staked a claim in the Data Science terrain. This article presents a few (actually nine) statistical principles for data scientists that have helped me, and continue to help me, when I work on complex interdisciplinary projects.

The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain and combinations of these. For inhomogeneous Poisson processes we consider Akaike's information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of ‘sample size’ needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.