STATISTICA & APPLICAZIONI - 2009 - 1

Inferential confidence intervals (CI) represent a widely used technique for testing the equality of the means of two Normal distributions by comparing two particular CI’s relative to the each mean. They allow simple graphic interpretations and result as being more informative than the traditional testing technique through the confidence levels. Yet they are unable to convey the information relative to the compatibility of the null hypothesis with the observed data usually provided by the p-value. The present paper identifies a new measure of such compatibility in the context of inferential CI’s and extends the technique to the non Normal case. Moreover, in case the null hypothesis is accepted, the problem of estimating the common mean is dealt with by means of the bounds of specific inferential CI’s. The proposed procedures are then applied to real data relative to foreign populations originating outside the European Union and sampled from the Italian territory.

In wildlife population studies one of the main goals is estimating the population density. Line transect sampling is a well established methodology for this purpose. The usual approach for estimating the density of the population of interest is to assume a particular model for the detection function. The estimates are extremely sensitive to the shape of the detection function, particularly to the socalled shoulder condition, which ensures that an animal is nearly certain to be detected if it is at a small distance from the observer. For instance, the half-normal model satisfies this condition whereas the negative exponential does not. So, testing whether the shoulder condition is consistent with the data is a primary concern. Since the problem of testing such a hypothesis is invariant under the group of scale transformations, in this paper we propose the uniformly most powerful test in the class of the scale invariant tests for the half-normal model against the negative exponential model. The asymptotic distribution of the test statistic is derived. The critical values and the power are tabulated via Monte Carlo simulations for small samples.

In this paper, we propose several initial values for the EM algorithm of maximum likelihood estimates of the parameters in a class of models, called CUB, recently introduced for ordinal data. Specifically, we compare the algorithmic efficiency of each estimator with respect to a naive proposal through a vast simulation experiment. The results confirm a substantial gain in efficiency of the moments estimators over the whole parametric space. Then, some extensions are also discussed and several applications to real data sets are presented.

Data heterogeneity, within a (linear) regression framework, often suggest the use of a Clusterwise Linear Regression (CLR) procedure, which implies, among other things, the estimate of the appropriate number of clusters as well as the cluster membership of each unit. The approaches to the estimation of a CLR model are essentially based on the Ordinary Least Square (OLS) criterion or the likelihood criterion. In this paper, in a context of OLS approach, we propose an estimation of the model making use of an algorithm based on a threshold criterion for the determination coefficient of each cluster, to identify the appropriate number of clusters, and of a modified Spath’s algorithm, to estimate the cluster membership of each sample unit. A simulation design and an application to a real data-set show that the procedure outperforms other algorithms commonly used in literature.

Motivated by the misspecification problem in time series analysis, the nonparametric approach has quickly developed in the latest years. First models in literature were focused on the estimation of the conditional mean. It is well known that alongside the conditional mean it is important to study the series volatility (conditional variance). The following paper deals with nonparametric autoregression with multiplicative volatility and additive mean as studied by Yang et al. (1999). A new estimation procedure is here provided. The procedure uses the residual-based estimator, backfitting algorithm and the local polynomial estimation. Some applications with simulated and real data will be presented.

After the Basel II accord, banks should not distribute funds without considering which sector firms belong to, as usually done. In this context, we would like to compare firm sector for what concern different financial ratios. Through a suitable multivariate nonparametric test we evaluate whether or not sectors can be distinguished with respect to the ratios. The analysis of a data set about positions from a medium size Italian financial institution clearly contradict the common banking practice of distributing funds without considering which sector firms belong to and strongly recommend for alternative credit treatment.

In modern socio-economic systems, often the aim of a performance analysis or quality evaluation is to compare different products, different manufacturing plants or service centres, different actions or distinct treatments. The question is, ‘‘Which is better?’’ This is complicated because the considered aspects are often measured through categorical data and the results can be affected by confounding factors. To solve this problem we discuss some directional permutation tests based on the nonparametric combination of dependent permutation tests (NPC) for two-sample comparisons in the presence of ordinal categorical variables and confounding factors. In particular we present a new permutation test based on the combination of a finite number of sample moments. To reduce the confounding effects we consider the joint application of stratification and the NPC method. We also show the results of Monte Carlo simulations in order to compare permutation solutions with other nonparametric tests and to evaluate the robustness of the test based on moments.