Australian & New Zealand Journal of Statistics最新文献

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.

This paper is concerned with the formulation of $��N�$-mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses time-to-first-detection within the context of detection/non-detection and time-to-each-detection and time-to-first-detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed-form expressions for the likelihoods associated with time-to-detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times-to-detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times-to-detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times-to-detection in addition to the count data. An R package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice.

The performance, in terms of coverage and expected length, of the model averaged tail area (MATA) confidence interval, proposed by Turek & Fletcher (2012, Computational Statistics & Data Analysis, 56, 2809–2815), depends greatly on the data-based model weights used in its construction. We generalise the computationally convenient exact formulae due to Kabaila, Welsh & Abeysekera (2016, Scandinavian Journal of Statistics, 43, 35–48) for the coverage and expected length of this confidence interval for two nested linear regression models to the case of two or more nested linear regression models. This permits the numerical assessment of the performance, in terms of coverage probability and scaled expected length, of the MATA confidence interval for any given data-based model weights in the context of three or more nested linear regression models. We illustrate this numerical assessment of performance of the MATA confidence interval, for model weights based on any given Generalised Information Criterion, in the context of three nested linear regression models using the real life ‘Cholesterol’ data. This provides a very informative further exploration of the influence of these model weights on the performance of this confidence interval.

We consider the problem of evaluating designs for a two-arm randomised experiment with an incidence (binary) outcome under a non-parametric general response model. Our two main results are that the a priori pair matching design is (1) the optimal design as measured by mean squared error among all block designs which includes complete randomisation. And (2), this pair-matching design is minimax, that is, it provides the lowest mean squared error under an adversarial response model. Theoretical results are supported by simulations and clinical trial data where we demonstrate the superior performance of pairwise matching designs under realistic conditions.

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian non-parametric regression. This problem becomes even more difficult when considering other families such as binary, Poisson and negative binomial regression. We present a novel method aiming to correct for measurement error when estimating regression functions. Our approach is sufficiently flexible to cover virtually all distributions and link functions regularly considered in generalised linear models. This approach depends on approximating the first and the second moment of the response after integrating out the true unobserved predictors in any semi-parametric generalised regression model. By the latter is meant a model with both linear and non-parametric effects that are connected to the mean response by a link function and with a response distribution in an exponential family or quasi-likelihood model. Unlike previous methods, the method we now propose is not restricted to truncated splines and can utilise various basis functions. Moreover, it can operate without making any distributional assumption about the unobserved predictor. Through extensive simulation studies, we study the performance of our method under many scenarios.