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Pericleous, Katerina; Kounias, Stratis
doi: 10.1080/03610926.2011.607533pmid: N/A
Row and column designs are examined and the concept of majorization is applied to find optimal designs, when the observations are either independent or dependent. The dependence follows a first-order autoregression with parameter α. The case of two treatments is examined and the universally optimal or Φ-optimal designs are given, for different values of a, when the number of experimental units is even or odd. A filtering procedure is followed to reduce the number of competing designs.
doi: 10.1080/03610926.2011.617482pmid: N/A
Consider a process defined as where 𝔹 is the backward operator, Q a polynomial with all zeros of modulus ≥1, and (Y t ) an ergodic stationary process. We show that , even if some zeros (real or complex) have modulus 1. In particular, if (Y t ) is a white noise, it becomes the innovation of (X t ). It follows that the polynomial regression model where P is a polynomial of degree p and (ϵ t ) is a white noise, is a zero-mean IMA(p + 1, p + 1) and that (ϵ t ) is the innovation of the MA part. A practical consequence of this fact is that the ARIMA model remains competitive even if the model is a genuine polynomial regression. Various numerical simulations illustrate that point.
doi: 10.1080/03610926.2011.605237pmid: N/A
We describe diverse stochastic inference problems whose solution essentially depends on the moment determinacy of some distributions involved. For a variety of stochastic models we ask questions such as “how to identify a distribution if knowing its moments?” “how asymmetric can be a distribution with zero odd order moments?” “is any mixture model identifiable?” For specific models we provide answers, motivating arguments, and illustrations. Some challenging open questions are outlined.
Bonnini, Stefano; Piccolo, Domenico; Salmaso, Luigi; Solmi, Francesca
doi: 10.1080/03610926.2011.590915pmid: N/A
In statistical surveys, people are often asked to express evaluations on several topics or to make an ordered arrangement in a list of objects (items, services, sentences, etc.); thus, the analysis of ratings and rankings is receiving a growing interest in many fields. In this framework, we develop a testing procedure for a class of mixture models with covariates (defined as CUB models), proposed by Piccolo (2003) and D'Elia and Piccolo (2005) and generally developed in a parametric context. Instead, we propose a nonparametric solution to perform inference on CUB models, specifically on the coefficients of the covariates. A simulation study proves that this approach is more appropriate in some specific data settings, mostly for small sample sizes.
doi: 10.1080/03610926.2011.615439pmid: N/A
The network of student transfers within the system of the University of Bologna adapts a constraint scale-free topology. Despite the presence of “hubs,” their role is strongly influenced by different institutional decisions and choices applied to courses. Therefore, the macro model of this network is not useful for previewing its evolution over time, particularly in the creation of critical points, which are courses with high out transfer rates. The idea is to introduce a probability of transfer function for each course, in order to preview the creation of critical points. The proposed model is fundamentally a binary regression logistic model. This rough model allows us to identify the possible creation of critical points in our complex system, these being “escape” courses, and to preview the impact of institutional decisions. At the same time, it may suggest how to remove the existing critical points in order to optimize the academic courses on offer.
Melas, Viatcheslav B.; Shpilev, Petr
doi: 10.1080/03610926.2011.615972pmid: N/A
The present article is devoted to an extension of the functional approach elaborated in the book Melas (2006) for studying optimal designs in linear and nonlinear regression models. Here we consider Bayesian efficient designs for nonlinear models under the standard assumptions on the observational errors. Sufficient conditions for uniqueness of locally optimal and Bayesian efficient designs for common optimality criteria are given. L-efficient Bayesian designs are constructed and investigated for a special nonlinear regression model of a rational form as an illustration of our main results. This model is interesting in both a practical and a theoretical sense.
Atlagh, M.; Broniatowski, M.; Celant, G.
doi: 10.1080/03610926.2011.593286pmid: N/A
This article provides the distribution of the last exit for strongly consistent estimators. Namely, we consider a small neighborhood of the (almost sure) limit and state the asymptotic distribution of the last time the estimator is outside this neighborhood. Such problems have been considered in the literature by various authors; this article extends these results in a semi-parametric frame. An application to adaptive estimation is provided.
doi: 10.1080/03610926.2011.589956pmid: N/A
In Measurement System Analysis a relevant issue is how to find confidence intervals for the parameters used to evaluate the capability of a gauge. In literature approximate solutions are available but they produce so wide intervals that they are often not effective in the decision process. In this article we introduce a new approach and, with particular reference to the parameter γR, i.e., the ratio of the variance due to the process and the variance due to the instrument, we show that, under quite realistic assumptions, we obtain confidence intervals narrower than other methods. An application to a real microelectronic case study is reported.
Matteucci, Mariagiulia; Mignani, Stefania; Veldkamp, Bernard P.
doi: 10.1080/03610926.2011.639973pmid: N/A
The focus of this article is on the choice of suitable prior distributions for item parameters within item response theory (IRT) models. In particular, the use of empirical prior distributions for item parameters is proposed. Firstly, regression trees are implemented in order to build informative empirical prior distributions. Secondly, model estimation is conducted within a fully Bayesian approach through the Gibbs sampler, which makes estimation feasible also with increasingly complex models. The main results show that item parameter recovery is improved with the introduction of empirical prior information about item parameters, also when only a small sample is available.
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