Inspired by constructing large‐size cointegrated portfolios, this paper considers a vector error correction model and develops the adaptive Lasso estimator of the cointegrating vectors. The asymptotic properties of the estimators and the oracle property of the adaptive Lasso are derived. An optimisation algorithm for estimating the model parameters is proposed. The simulation study shows the effectiveness

Empirical likelihood (EL) has been extensively studied to make statistical inferences for independent and dependent observations. However, it experiences the problem of under‐coverage which causes the coverage probability of the EL‐based confidence intervals to be lower than the nominal level, especially in small sample sizes. In this paper, we propose modified versions of different EL‐related methods

In this article, we study the statistical properties of the goodness‐of‐fit measure mpp proposed by (Eshima & Tabata 2007, Statistics & Probability Letters 77, 583–593) for generalised linear models. Focusing on the special case of Poisson regression using the canonical log link function, and assuming a random vector X of covariates, we obtain an explicit form for mpp that enables us to study its properties

Universal and individual two‐sided tolerance intervals that take the inherent structure of normal mixture distributions into account are introduced in this paper for the purpose of monitoring the overall population and specific subpopulations. On the basis of generalised fiducial inference, a Markov chain Monte Carlo sampler is proposed to generate realisations from the generalised fiducial distributions

This R package determines optimal stratification of univariate populations under stratified sampling designs using a parametric‐based method. It determines the optimum strata boundaries (OSB), optimum sample sizes (OSS) and multiple other quantities for the study variable, y, using the best‐fit probability density function of a study variable available from survey data. The method requires the parameters

Clinical work is characterised by frequent interjection of external prompts causing clinicians to switch from a primary task to deal with an incoming secondary task, a phenomenon associated with negative effects in experimental studies. This is an important yet underexplored aspect of work in safety critical settings in general, since an increase in task length due to task‐switching implies reduced

Predicting the arrival time of a transit vehicle involves not only knowledge of its current position and schedule adherence, but also traffic conditions along the remainder of the route. Road networks are dynamic and can quickly change from free‐flowing to highly congested, which impacts the arrival time of transit vehicles, particularly buses which often share the road with other vehicles, so reliable

We examine the relationships between electoral socio‐demographic characteristics and two‐party preferences in the six Australian federal elections held between 2001 and 2016. Socio‐demographic information is derived from the Australian Census which occurs every 5 years. Since a census is not directly available for each election, an imputation method is employed to estimate census data for the electorates

Multivariate distributions are more and more used to model the dependence encountered in many fields. However, classical multivariate distributions can be restrictive by their nature, while Sarmanov's multivariate distribution, by joining different marginals in a flexible and tractable dependence structure, often provides a valuable alternative. In this paper, we introduce some bivariate mixed Sarmanov

In longitudinal data where the timing and frequency of the measurement of outcomes may be associated with the value of the outcome, significant bias can occur. Previous results depended on correct specification of the outcome process and a somewhat unrealistic visit process model. In practice, this will never exactly be the case, so it is important to understand to what degree the results hold when

In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error

A folded type model is developed for analysing compositional data. The proposed model involves an extension of the α‐transformation for compositional data and provides a new and flexible class of distributions for modelling data defined on the simplex sample space. Despite its rather seemingly complex structure, employment of the EM algorithm guarantees efficient parameter estimation. The model is

In recent years, modelling count data has become one of the most important and popular topics in time‐series analysis. At the same time, variable selection methods have become widely used in many fields as an effective statistical modelling tool. In this paper, we consider using a variable selection method to solve a modelling problem regarding the first‐order Poisson integer‐valued autoregressive

Pitman medal awarded by Statistical Society of Australia for outstanding achievement.

This paper considers modelling of a non‐stationary bivariate integer‐valued autoregressive process of order 1 (BINAR(1)) where the cross‐dependence between the counting series is formed through the relationship of the current series with the previous‐lagged count series observations while the pair of innovations is independent and marginally Poisson. In addition, this paper proposes a generalised quasi‐likelihood

In outcome‐dependent sampling, the continuous or binary outcome variable in a regression model is available in advance to guide selection of a sample on which explanatory variables are then measured. Selection probabilities may either be a smooth function of the outcome variable or be based on a stratification of the outcome. In many cases, only data from the final sample is accessible to the analyst

A generalised regression estimation procedure is proposed that can lead to much improved estimation of population characteristics, such as quantiles, variances and coefficients of variation. The method involves conditioning on the discrepancy between an estimate of an auxiliary parameter and its known population value. The key distributional assumption is joint asymptotic normality of the estimates

Data from large surveys are often supplemented with sampling weights that are designed to reflect unequal probabilities of response and selection inherent in complex survey sampling methods. We propose two methods for Bayesian estimation of parametric models in a setting where the survey data and the weights are available, but where information on how the weights were constructed is unavailable. The

The score test statistic from the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the likelihood‐ratio test and the Wald test. However, several authors have noted that under the alternative hypothesis this no longer holds and in particular the score

Negative binomial (NB) regression is the most common full‐likelihood method for analysing count data exhibiting overdispersion with respect to the Poisson distribution. Usually most practitioners are content to fit one of two NB variants, however other important variants exist. It is demonstrated here that the VGAMR package can fit them all under a common statistical framework founded upon a generalised

Peter Hall's work illuminated many aspects of statistical thought, some of which are very well known including the bootstrap and smoothing. However, he also explored many other lesser known aspects of mathematical statistics. This is a survey of one of those areas, initiated by a seminal paper in 2005, on high dimension low sample size asymptotics. An interesting characteristic of that first paper

Consider the classical Gaussian unitary ensemble of size N and the real white Wishart ensemble with N variables and n degrees of freedom. In the limits of large N and n, with positive ratio γ in the Wishart case, the expected number of eigenvalues that exit the upper bulk edge is less than one, approaching 0.031 and 0.170 respectively, the latter number being independent of γ. These statements are

A multi-sample test for equality of mean directions is developed for populations having Langevin-von Mises-Fisher distributions with a common unknown concentration. The proposed test statistic is a monotone transformation of the likelihood ratio. The high-concentration asymptotic null distribution of the test statistic is derived. In contrast to previously suggested high-concentration tests, the high-concentration

Quadratic forms capture multivariate information in a single number, making them useful, for example, in hypothesis testing. When a quadratic form is large and hence interesting, it might be informative to partition the quadratic form into contributions of individual variables. In this paper it is argued that meaningful partitions can be formed, though the precise partition that is determined will

Investigators often gather longitudinal data to assess changes in responses over time within subjects and to relate these changes to within-subject changes in predictors. Missing data are common in such studies and predictors can be correlated with subject-specific effects. Maximum likelihood methods for generalized linear mixed models provide consistent estimates when the data are `missing at random'

We extend the standard multivariate mixed model by incorporating a smooth time effect and relaxing distributional assumptions. We propose a semiparametric Bayesian approach to multivariate longitudinal data using a mixture of Polya trees prior distribution. Usually, the distribution of random effects in a longitudinal data model is assumed to be Gaussian. However, the normality assumption may be suspect

A new function for the competing risks model, the conditional cumulative hazard function, is introduced, from which the conditional distribution of failure times of individuals failing due to cause j can be studied. The standard Nelson-Aalen estimator is not appropriate in this setting, as population membership (mark) information may be missing for some individuals owing to random right-censoring.

This paper considers statistical inference for partially linear models Y = X(T)mu + nu(Z) + epsilon when the linear covariate X is missing with missing probability pi depending upon (Y, Z). We propose empirical likelihood based statistics to construct confidence regions for beta and nu(z). The resulting statistics are shown to be asymptotically chi-squared distributed. Finite sample performance of