Australian & New Zealand Journal of Statistics最新文献

Functional sliced inverse regression (FSIR) is the among most popular methods for the functional dimension reduction. However, FSIR has two evident shortcomings. On the one hand, the number of samples in each slice must not be too small and selecting a suitable S is difficult, particularly for data with small sample size, where S indicates the number of slices. On the other hand, FSIR and its related methods are well-known for their poor performance when the link function is an even (or symmetric) dependency. To solve these two problems, we propose three new types of estimation methods. First, we propose the functional fuzzy inverse regression (FFIR) method based on a fuzzy partition. Compared with FSIR that uses a hard partition, the fuzzy partition uses all samples with different weights to estimate the mean in each slice. Therefore, FFIR exhibits good performance even for data with small sample size. Second, we suggest two transformation approaches, namely, FSIRR and FSIRP, avoiding the symmetric dependency between the response and the predictor. FSIRR eliminates the symmetric dependency by transforming the response variable, while FSIRP overcomes the symmetric dependency by transforming the functional predictor. Third, we propose the FFIRR and FFIRP methods by combining the advantages of FFIR and two transformation methods. FFIRR and FFIRP replace the FSIR method on the transformation data via FFIR. Simulation and real data analysis show that three types of proposed methods exhibit better performance than FSIR in terms of the estimation accuracy and stability.

We focus on regression models that consist of (i) a model for the conditional mean of the outcome and (ii) a distributional assumption about the distribution of the outcome, both conditional on the regressors. Generalised linear models form a well-known example. The choice of the outcome distribution is often motivated by prior or background knowledge of the researcher, or it is simply chosen for convenience. We propose smooth goodness of fit tests for testing the distributional assumption in regression models. The tests arise from embedding the regression model in a smooth family of alternatives, and constructing appropriate score tests that correctly account for nuisance parameter estimation. The tests are customised, focussed and comprehensive. We present several examples to illustrate the wide applicability of our method. A small simulation study demonstrates that our tests have power to detect important deviations from the hypothesised model.

Generalised statistical distributions have been widely used over the last decades for modelling phenomena in different fields. The generalisations have been made to produce distributions with more flexibility and lead to more accurate modelling in practice. Statistical analysis of the generalised distributions requires new statistical packages. The Newdistns package due to Nadarajah and Rocha provides R routines with functionality to compute probability density function (PDF), cumulative distribution function (CDF), quantile function, random numbers and parameter estimates of 19 families of distributions with applications in survival analysis. Here, we introduce an R package, called MPS, for computing PDF, CDF, quantile function, random numbers, Q–Q plots and parameter estimates for 24 shifted new families of distributions. By considering an extra location parameter, each family will be defined on the whole real line and so covers a broader range of applicability. We adopt the well-known maximum product spacing approach to estimate parameters of the families because under some situations the maximum likelihood (ML) estimators fail to exist. We demonstrate MPS by analysing two well-known real data sets. For the first data set, the ML estimators break down, but MPS works well. For the second set, adding a location parameter results in a reasonable model while the absence of the location parameter makes the model quite inappropriate. The MPS is available from CRAN at https://cran.r-project.org/package=MPS.

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a single-index structure, while the other is included linearly through the high-dimensional vector formed by its discretised observations. For this model, two new algorithms are presented for selecting relevant variables in the linear part and estimating the model. Both procedures utilise the functional origin of linear covariates. Finite sample experiments demonstrated the scope of application of both algorithms: the first method is a fast algorithm that provides a solution (without loss in predictive ability) for the significant computational time required by standard variable selection methods for estimating this model, and the second algorithm completes the set of relevant linear covariates provided by the first, thus improving its predictive efficiency. Some asymptotic results theoretically support both procedures. A real data application demonstrated the applicability of the presented methodology from a predictive perspective in terms of the interpretability of outputs and low computational cost.

Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data without a strong competitor having the same main features. A class of normalised inverse-Gaussian (N-IG) process was introduced in the literature and has been explored in the Bayesian context as a powerful alternative to the Dirichlet process. Until this moment, no attention has been paid to the univariate N-IG distribution in the classical inference. In this paper, we propose the bessel regression based on the univariate N-IG distribution, which is an alternative to the beta model. The estimation of the parameters is done through an expectation–maximisation (EM) algorithm and the paper discusses how to perform inference. A useful and practical discrimination procedure is proposed for model selection between bessel and beta regressions. A new R package called bbreg is developed for fitting both bessel and beta regression models based on the EM-algorithm and further providing graphical tools for model adequacy and model selection as well. Proper documentation for this package is available. The performances of the models are evaluated under misspecification in a simulation study. An empirical illustration is explored to confront results from bessel and beta regressions by using the new R package bbreg.

The evaluation of the teaching efficiency, under different points of view, is an important aspect for the university system because it helps managers to improve more and more the quality of the education and helps students to achieve strong professional skills. In this framework, students’ careers as well as teachers’ qualification and quantity adequacy indicators are analysed based on data sets provided by the Italian National Agency for the Evaluation of Universities and Research Institutes (ANVUR) according to a mixture model approach. In particular, parsimonious mixtures of matrix-normal distributions are used to detect underlying grouping structures. The results show that the data present an underlying group structure of courses having different traits, thus providing useful information for the university policy makers.