Australian & New Zealand Journal of Statistics最新文献

We investigate the use of multiple linked lists for population size estimation and to estimate the relationships between covariates appearing on the lists. Over the lists, the covariates aim to measure the same concept. The relationships between the covariates are not fully known because of missing values on the covariates: some cases do not appear in some lists; some cases are on one or more of the lists but have missing covariate values on some of the lists; and some cases are not observed in any list. In earlier work, multiple system estimation has been combined with latent class analysis to give a consensus estimate where an underlying dichotomous categorical covariate is measured differently in different lists. This was applied to ethnicity covariates in New Zealand with two levels, Māori and non-Māori. In this paper, we apply this approach to ethnicity covariates with a larger number of categories, and find that it produces satisfactory results with four categories. We assess the purity of the latent classes using entropy and conditional probability measures. We also examine the evolution of annual estimates from multiple lists (where one list is the population census) over 2013–2020, finding that the estimated latent class proportions are very stable. We assess the impact of disclosure control measures on the outputs.

Fused lasso regression is a popular method for identifying homogeneous groups and sparsity patterns in regression coefficients based on either the presumed order or a more general graph structure of the covariates. However, the traditional fused lasso may yield misleading outcomes in the presence of outliers. In this paper, we propose an extension of the fused lasso, namely the robust adaptive fused lasso (RAFL), which pursues homogeneity and sparsity patterns in regression coefficients while accounting for potential outliers within the data. By using Huber's loss or Tukey's biweight loss, RAFL can resist outliers in the responses or in both the responses and the covariates. We also demonstrate that when the adaptive weights are properly chosen, the proposed RAFL achieves consistency in variable selection, consistency in grouping and asymptotic normality. Furthermore, a novel optimization algorithm, which employs the alternating direction method of multipliers, embedded with an accelerated proximal gradient algorithm, is developed to solve RAFL efficiently. Our simulation study shows that RAFL offers substantial improvements in terms of both grouping accuracy and prediction accuracy compared with the fused lasso, particularly when dealing with contaminated data. Additionally, a real analysis of cookie data demonstrates the effectiveness of RAFL.

Misspecification of the error covariance in linear models usually leads to incorrect inference and conclusions. We consider two linear models, $��A�$and $��B�$, with the same design matrix but different error covariance matrices. The conditions under which every representation of the best linear unbiased estimator (BLUE) of any estimable parametric vector under $��A�$ remains BLUE under $��B�$have been well known since C.R. Rao's paper in 1971: Unified theory of linear estimation, Sankhyā Ser. A, Vol. 33, pp. 371–394. However, there are no previously published results on retaining the weighted sum of squares of errors (SSE) for non-full-rank design or error covariance matrices, and the question of when the covariance matrix of the BLUEs is also retained has been partially explored only recently. For change in any specified error covariance matrix, we provide necessary and sufficient conditions (nasc) for both BLUEs and their covariance matrix to remain unaltered and to retain this property for all submodels. We also consider nasc for SSE to be unchanged. We decompose SSE under error covariance changes, and derive nasc under which error covariance change leaves hypothesis tests for fixed-effect deletion under normality unaltered. We also show that simultaneous retention of BLUEs and both their covariance and SSE is not possible. We outline the effects of weak and strong error covariance singularity. We provide applications (via data cloning) to maintaining data confidentiality in Official Statistics without using Confidentialised Unit Record Files (CURFs), to certain types of experimental design and to estimation of fixed parameters for linear models for single nucleotide polymorphisms (SNPs) in genetics.

Classically, the distinction between a fixed versus a random factor in analysis of variance has been considered a binary choice. Here we consider that any given factor can also occur along an incremental series of steps between these two extremes, depending on the sampling fraction of its levels from the wider population. Fixed factors occur where all possible levels are drawn, and random factors occur in the limit as the population of possible levels approaches infinity. When some identifiable fraction of a finite population of possible levels is drawn, the factor can be thought of as something in between fixed and random, and can be analysed explicitly as finite directly within the analysis of variance (ANOVA) framework. Requiring explicit specification of the population size from which observed levels are drawn for each factor, we provide a unified approach to derive expectations of mean squares (EMS) in ANOVA for any types of factors along the entire graded progression from fixed to random, inclusive, that may be nested within or crossed with one another, from balanced, asymmetrical or unbalanced designs, including multi-level hierarchical sampling designs, mixed models and interactions. Implications for estimation of variance components, tailored bootstrap methods and tests of hypotheses under minimal assumptions of exchangeability are described and further extended to multivariate dissimilarity-based settings.

When modelling the association between the ordinal categorical variables of a contingency table, ordinal log-linear models are typically used; these models are a variation of the more popular log-linear model, which has attracted considerable attention in the statistics and allied literature since the late 1960s. Estimating the parameters of an ordinal log-linear model usually involves the use of iterative techniques, typically Newton's method and iterative proportional fitting. However, the early 2000s brought with it more direct estimation methods that do not require the use of iterative techniques. When the focus is on the parameter that reflects the linear-by-linear association between the variables, these methods have proven to provide unbiased, consistent and normally distributed estimates. Despite this new work, no attention has been given to the estimation of the least-squares estimator. Therefore, this article derives the least-squares estimator of the linear-by-linear association parameter and shows it to be equivalent to one of the existing non-iterative estimators recently described. We also derive two further least-squares estimators based on the Box-Cox transformation and derive their variance.